13 - Measurability: Borel Isomorphism and Analytic Sets pp. 487-502
By R. M. Dudley
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Real Analysis and Probability
Second edition
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R. M. Dudley
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Publisher: Cambridge University Press
Print Publication Year: 2002
Online Publication Date:July 2010
Online ISBN:9780511755347
Hardback ISBN:9780521809726
Paperback ISBN:9780521007542
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Chapter DOI: http://dx.doi.org/10.1017/CBO9780511755347.014
Subjects: Probability theory and stochastic processes, Real and Complex Analysis
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pp. i-iv
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pp. v-viii
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Preface to the Cambridge Edition: Read PDF
pp. ix-x
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1 - Foundations; Set Theory: Read PDF
pp. 1-23
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2 - General Topology: Read PDF
pp. 24-84
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pp. 85-113
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pp. 114-151
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5 - Lp Spaces; Introduction to Functional Analysis: Read PDF
pp. 152-187
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6 - Convex Sets and Duality of Normed Spaces: Read PDF
pp. 188-221
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7 - Measure, Topology, and Differentiation: Read PDF
pp. 222-249
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8 - Introduction to Probability Theory: Read PDF
pp. 250-281
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9 - Convergence of Laws and Central Limit Theorems: Read PDF
pp. 282-335
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10 - Conditional Expectations and Martingales: Read PDF
pp. 336-384
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11 - Convergence of Laws on Separable Metric Spaces: Read PDF
pp. 385-438
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12 - Stochastic Processes: Read PDF
pp. 439-486
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13 - Measurability: Borel Isomorphism and Analytic Sets: Read PDF
pp. 487-502
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Appendix A - Axiomatic Set Theory: Read PDF
pp. 503-520
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Appendix B - Complex Numbers, Vector Spaces, and Taylor's Theorem with Remainder: Read PDF
pp. 521-525
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Appendix C - The Problem of Measure: Read PDF
pp. 526-527
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Appendix D - Rearranging Sums of Nonnegative Terms: Read PDF
pp. 528-529
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Appendix E - Pathologies of Compact Nonmetric Spaces: Read PDF
pp. 530-540
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pp. 541-545
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pp. 546-553
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pp. 554-555
Reference Title: References
Reference Type: reference-list
- Boorman, Kathleen E., Barbara E. Dodd, and Patrick J. Lincoln (1977). Blood Group Serology. 5th ed. Churchill Livingstone, Edinburgh
- *Borel, Émile (1898). LeÇons sur la théorie des fonctions. Gauthier-Villars, Paris
- Cantor, Georg (1874). Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen. Journal für die reine u. angew. Math. 77: 258-262
- Cantor, Georg (1892). Über eine elementare Frage der Mannigfaltigkeitslehre. Jahresbericht der deutschen Mathematiker-Vereinigung 1: 75-78
- Fraenkel, Abraham A. (1976). Abstract Set Theory. Rev. by Azriel Levy. 4th ed. North-Holland, Amsterdam
- Frewer, Magdalene (1978). Das wissenschaftliche Werk Felix Bernsteins. Diplomarbeit, Inst. f. Math. Statistik u. Wirtschaftsmath., Univ. Göttingen
- Hausdorff, Felix (1914). Grundzüge der Mengenlehre. Von Veit, Leipzig. 1st ed. repr. Chelsea, New York (1949). 2d ed., 1927. 3d ed., 1937, published in English as Set Theory, transl. J. R. Aumann et al., Chelsea, New York (1957; 2d Engl. ed., 1962; 3d Engl. ed., 1978)
- Jech, Thomas (1973). The Axiom of Choice. North-Holland, Amsterdam
- Korselt, A. (1911). Über einen Beweis des Äquivalenzsatzes. Math. Annalen 70: 294-296
- Nathan, Henry (1970). Bernstein, Felix. In Dictionary of Scientific Biography 2: 58–59. Scribner's, New York
- Rubin, Herman, and Jean E. Rubin (1963). Equivalents of the Axiom of Choice. North-Holland, Amsterdam. 2d. ed. 1985
- Russell, Bertrand (1906). On some difficulties in the theory of transfinite numbers and order types. Proc. London Math. Soc. (Ser. 2) 4: 29-53
- Zermelo, Ernst (1904). Beweis, dass jede Menge wohlgeordnet werden kann. Math. Annalen 59: 514-516
- Zermelo, Ernst (1908a). Neuer Beweis für die Möglichkeit einer Wohlordnung. Math. Ann. 65: 107-128
- Zermelo, Ernst (1908b). Untersuchungen über die Grundlagen der Mengenlehre I. Math. Ann. 65: 261-281
- Zorn, Max (1935). A remark on method in transfinite algebra. Bull. Amer. Math. Soc. 41: 667-670
Reference Title: References
Reference Type: reference-list
- Abel, Niels Henrik (1826). Untersuchungen über die Reihe J. reine angew. Math. 1: 311–339. Also in Oeuvres complètes, ed. L. Sylow and S. Lie. Grɸndahl, Kristiania [Oslo], 1881, I, pp. 219–250
- Alexandroff, Paul [Aleksandrov, Pavel Sergeevich] (1924). Sur les ensembles de la première classe et les espaces abstraits. Comptes Rendus Acad. Sci. Paris 178: 185–187
- Alexandroff, Paul [Aleksandrov, Pavel Sergeevich](1926). Über stetige Abbildungen kompakter Räume. Math. Annalen 96: 555–571
- Alexandroff, Paul [Aleksandrov, Pavel Sergeevich](1950). Pavel Samuilovich Urysohn. Uspekhi Mat. Nauk 5, no. 1: 196–202
- Alexandroff, Paul [Aleksandrov, Pavel Sergeevich] et al. (1967). Andrei Nikolaevich Tychonov (on his sixtieth birthday): On the works of A. N. Tychonov in. … Uspekhi Mat. Nauk 22, no. 2: 133–188 (in Russian); transl. in Russian Math. Surveys 22, no. 2: 109–161
- Alexandroff, Paul [Aleksandrov, Pavel Sergeevich] and V. V. Fedorchuk, with the assistance of V. I. Zaitsev (1978). The main aspects in the development of set-theoretical topology. Russian Math. Surveys 33, no. 3: 1–53. Transl. from Uspekhi Mat. Nauk 33, no. 3 (201): 3–48 (in Russian)
- Alexandroff, Paul [Aleksandrov, Pavel Sergeevich] and Heinz Hopf (1935). Topologie, 1. Band. Springer, Berlin; repr. Chelsea, New York, 1965
- Alexandroff, Paul [Aleksandrov, Pavel Sergeevich], A. Samarskii, and A. Sveshnikov (1956). Andrei Nikolaevich Tychonov (on his fiftieth birthday). Uspekhi Mat. Nauk 11, no. 6: 235–245 (in Russian)
- Alexandroff, Paul [Aleksandrov, Pavel Sergeevich] and Paul Urysohn (1923). Une condition nécessaire et suffisante pour qu'une classe () soit une classe (). C. R. Acad. Sci Paris 177: 1274–1276
- Alexandroff, Paul [Aleksandrov, Pavel Sergeevich andAlexandroff, Paul [Aleksandrov, Pavel Sergeevich (1924). Theorie der topologischen Räume. Math. Annalen. 92: 258–266
- Arboleda, L. C. (1979). Les débuts de 1'école topologique soviétique: Notes sur les lettres de Paul S. Alexandroff et Paul S. Urysohn à Maurice Fréchet. Arch. Hist. Exact Sci. 20: 73–89
- Arkhangelskii, A. V., A. N. Kolmogorov, A. A. Maltsev, and O. A. Oleinik (1976). Pavel Sergeevich Aleksandrov (On his eightieth birthday). Uspekhi Mat. Nauk 31, no. 5: 3–15 (in Russian); transl. in Russian Math. Surveys 31, no. 5: 1–13
- *Arzelà, Cesare (1882–1883). Un'osservazione intorno alle serie di funzioni. Rend. dell' Acad. R. delle Sci. dell'Istituto di Bologna, pp. 142–159
- **Arzelà, Cesare (1889). Funzioni di linee. Atti della R. Accad. dei Lincei, Rend. Cl. Sci. Fis. Mat. Nat. (Ser. 4) 5: 342–348
- **Arzelà, Cesare (1895). Sulle funzioni di linee. Mem. Accad. Sci. Ist. Bologna Cl. Sci. Fis. Mat. (Ser. 5) 5: 55–74
- *Ascoli, G. (1883–1884). Le curve limiti di una varietà data di curve. Atti della R. Accad. dei Lincei, Memorie della Cl. Sci. Fis. Mat. Nat. (Ser. 3) 18: 521–586
- Baire, René (1899). Sur les fonctions de variables réelles (Thèse). Annali di Matematica Pura ed Applic. (Ser. 3) 3: 1–123
- Baire, René (1906). Sur la représentation des fonctions continues. Acta Math. 30: 1–48
- Bartle, R. G. (1964). The Elements of Real Analysis. Wiley, New York
- Biermann, Kurt-R. (1976). Weierstrass, Karl Theodor Wilhelm. Dictionary of Scientific Biography 14: 219–224. Scribner's, New York
- *Bolzano, B. P. J. N. (1818). Rein analytischer Beweis des Lehrsatzes, dass zwischen je zwey Werthen, die ein entgegengesetztes Resultat gewähren, wenigstens eine reelle Wurzel der Gleichung liege. Abh. Gesell. Wiss. Prague (Ser. 3) 5: 1–60
- Borel, Émile (1895). Sur quelques points de la théorie des fonctions. Ann. Scient. Ecole Normale Sup. (Ser. 3) 12: 9–55
- Borsuk, Karol (1934). Über Isomorphie der Funktionalräume. Bull. Acad Polon. Sci. Lett. Classe Sci. Sér. A Math. 1933: 1–10
- Bourbaki, Nicolas [pseud.] (1940, 1948, 1953, 1961, 1971). Topologie Générale, Chap. 9. Utilisation des nombres réels en topologie générale. Hermann, Paris. English transl. Elements of Mathematics. General Topology, Part 2. Hermann, Paris; Addison-Wesley, Reading, Mass., 1966
- Cantor, Georg (1872). Ueber die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen. Math. Annalen 5: 123–132
- Cantor, Georg (1879–1883). Ueber unendliche, lineare Punktmannichfaltigkeiten. Math. Annalen 15: 1–7; 17: 355–358; 20: 113–121; 21: 51–58
- Caratheodory, Constantin (1913). Über die Begrenzung einfach zusammenhängender Gebiete. Math. Annalen 73: 323–370
- Caratheodory, Constantin (1918). Vorlesungen über reelle Funktionen. Teubner, Leipzig and Berlin. 2d ed., 1927
- Cartan, Henri (1937). Théorie des filtres: Filtres et ultrafiltres. C. R. Acad. Sci. Paris 205: 595–598, 777–779
- Cauchy, Augustin-Louis (1821). Cours d'analyse de l'école Royale Polytechnique, Paris
- Cauchy, Augustin-Louis (1823). Résumés des leÇadons données à l'école Royale Polytechnique sur le calcul infinitésimal. Debure, Paris; also in Oeuvres Complètes (Ser. 2), IV, pp. 5–261, Gauthier-Villars, Paris, 1889
- *Cauchy, Augustin-Louis (1833). Résumés analytiques. Imprimerie Royale, Turin
- Cauchy, Augustin-Louis (1853). Note sur les séries convergentes dons les divers termes sont des functions continues d'une variable réelle ou imaginaire, entre des limites données. Comptes Rendus Acad. Sci. Paris 36: 454–459. Also in Oeuvres Complètes (Ser. 1) Ⅻ, pp. 30–36. Gauthier-Villars, Paris, 1900
- Čech, Eduard (1936). Point Sets. In Czech, Bodové Množiny. 2d ed. 1966, Czech. Acad. Sci., Prague; *In English, transl. by AleŠ Pultr, Academic Press, New York, 1969
- Čech, Eduard (1937). On bicompact spaces. Ann. Math. (Ser. 2) 38: 823–844
- Čech, Eduard (1959). Topological Spaces. In Czech, *Topologické Prostory. Rev. English Ed. (1966), Eds. Z. FrolÍk and M. Katĕtov; Czech. Acad. Sci., Prague; Wiley, London
- Čech, Eduard (1968). Topological Papers of Eduard Čech. Academia (Czech. Acad. Sci), Prague
- Chernoff, Paul R. (1992). A simple proof of Tychonoff's theorem via nets. Amer. Math. Monthly 99: 932–934
- Chittenden, E. W. (1927). On the metrization problem and related problems in the theory of abstract sets. Bull. Amer. Math. Soc. 33: 13–34
- *Dini, Ulisse (1878). Fondamenti per la teorica delle funzioni di variabili reali. Nistri, Pisa
- *Dini, Ulisse (1953–1959>, posth.) Opere. 5 vols. Ediz. Cremonese, Rome
- Dugundji, James (1951). An extension of Tietze's theorem. Pacific J. Math. 1: 352–367
- Dugundji, James (1966). Topology. Allyn & Bacon, Boston
- Dunford, Nelson, and Jacob T. Schwartz, with the assistance of William G. Badé and Robert G. Bartle (1958). Linear Operators, Part I: General Theory. Interscience, New York
- Eichhorn, Eugen (1992). Felix Hausdorff—Paul Mongré. Some aspects of his life and the meaning of his death. In Gähler, W., Herrlich, H., and Preuβ, G., eds., Recent Developments of General Topology and its Applications; Internat. Conf. in Memory of Felix Hausdorff (1868–1942), Akademie Verlag, Berlin, pp. 85–117
- Feferman, Solomon (1964). Some applications of the notions of forcing and generic sets. Fund. Math. 56: 325–345
- Fréchet, Maurice (1906). Sur quelques points du calcul fonctionnel. Rendiconti Circolo Mat. Palermo 22: 1–74
- Fréchet, Maurice (1910). Les dimensions d'un ensemble abstrait. Math. Annalen 68: 145–168
- Fréchet, Maurice (1918). Sur la notion de voisinage dans les ensembles abstraits. Bull. Sci. Math. 42: 138–156
- Fréchet, Maurice (1928). Les espaces abstraits. Gauthier-Villars, Paris
- Frink, A. H. (1937). Distance functions and the metrization problem. Bull. Amer. Math. Soc. 43: 133–142
- Grattan-Guinness, I. (1970). The Development of the Foundations of Analysis from Euler to Riemann. MIT Press, Cambridge, MA
- Gudermann, Christof J. (1838). Theorie der Modular-Functionen und der Modular-Integrale, 4–5 Abschnitt. J. reine angew. Math. 18: 220–258
- Hahn, Hans (1921). Theorie der reellen Funktionen 1. Springer, Berlin
- Hardy, Godfrey H. (1916–1919). Sir George Stokes and the concept of uniform convergence. Proc. Cambr. Phil. Soc. 19: 148–156
- Hausdorff, Felix (1914). Grundzüge der Mengenlehre. Von Veit, Leipzig. (See References to Chap. 1 for later editions.)
- Hausdorff, Felix (1924). Die Mengen G_δ in vollständigen Räumen. Fund. Math. 6: 146–148
- Heine, E. [Heinrich Eduard] (1870). Ueber trigonometrische Reihen. Journal für die reine und angew. Math. 71: 353–365
- Heine, E. [Heinrich Eduard] (1872). Die Elemente der Functionenlehre. Journal für die reine und angew. Math. 74: 172–188
- Hoffman, Kenneth M. (1975). Analysis in Euclidean Space. Prentice-Hall, Englewood Cliffs, N. J.
- Kelley, John L. (1955). General Topology. Van Nostrand, Princeton
- Kisyński, J. (1959–1960). Convergence du type L. Colloq. Math. 7: 205–211
- Kolmogorov, A. N., L. A. Lyusternik, Yu. M. Smirnov, A. N. Tychonov, and S. V. Fomin (1966). Pavel Sergeevich Alexandrov (On his seventieth birthday and the fiftieth anniversary of his scientific activity). Uspekhi Mat. Nauk 21, no. 4: 2–7 (in Russian); transl. in Russian Math. Surveys 21, no. 4: 2–6
- Kuratowski, Kazimierz (1935). Quelques problèmes concernant les espaces métriques non-séparables. Fund. Math. 25: 534–545
- Kuratowski, Kazimierz (1958). Topologie, vol. 1. PWN, Warsaw; Hafner, New York
- Lebesgue, Henri (1904). Leçons sur l'intégration et la recherche des fonctions primitives. Gauthier-Villars, Paris
- Lebesgue, Henri (1907a). Sur le problème de Dirichlet. Rend. Circolo Mat. Palermo 24: 371–402
- Lebesgue, Henri (1907b). Review of Young and Young (1906). Bull. Sci. Math. (Ser. 2) 31: 129–135
- Manning, Kenneth R. (1975). The emergence of the Weierstrassian approach to complex analysis. Arch. Hist. Exact Sci. 14: 297–383
- *Mazurkiewicz, Stefan (1916). Über Borelsche Mengen. Bull. Acad. Cracovie 1916: 490–494
- Moore, E. H. (1915). Definition of limit in general integral analysis. Proc. Nat. Acad. Sci. USA 1: 628–632
- Moore, E. H. and H. L. Smith (1922). A general theory of limits. Amer. J. Math. 44: 102–121
- Osgood, W. F. (1897). Non-uniform convergence and the integration of series term by term. Amer. J. Math.19: 155–190
- Peano, G. (1890). Sur un courbe, qui remplit toute une aire plane. Math. Ann. 36: 157–160
- Pontryagin, L. S., and E. F. Mishchenko (1956). Pavel Sergeevich Aleksandrov (On his sixtieth birthday and fortieth year of scientific activity). Uspekhi Mat. Nauk 11, no. 4: 183–192 (in Russian)
- Reich, Karin (1973). Die Geschichte der Differentialgeometrie von Gauss bis Riemann (1828–1868). Arch. Hist. Exact Sci. 11: 273–382
- van Rootselaar, B. (1970). Bolzano, Bernard. Dictionary of Scientific Biography, II, pp. 273–279. Scribner's, New York
- *Seidel, Phillip Ludwig von (1847–1849). Note über eine Eigenschaft der Reihen, welche discontinuierliche Functionen darstellen. Abh. der Bayer. Akad. der Wiss. (Munich) 5: 379–393
- Siegmund-Schultze, Reinhard (1982). Die Anfänge der Funktionalanalysis und ihr Platz im Umwälzungsprozess der Mathematik um 1900. Arch. Hist. Exact Sci. 26: 13–71
- Stokes, George G. (1847–1848). On the critical values of periodic series. Trans. Cambr. Phil. Soc. 8: 533–583; Mathematical and Physical Papers I: 236–313
- Stone, Marshall Harvey (1936). The theory of representations for Boolean algebras. Trans. Amer. Math. Soc. 40: 37–111
- Stone, Marshall Harvey(1937). Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc. 41: 375–481
- Stone, Marshall Harvey (1947–48). The generalized Weierstrass approximation theorem. Math. Mag. 21: 167–184, 237–254. Repr. in Studies in Modern Analysis 1, ed. R. C. Buck, Math. Assoc. of Amer., 1962, pp. 30–87
- Temple, George (1981). 100 Years of Mathematics. Springer, New York
- Tietze, Heinrich (1915). Über Funktionen, die auf einer abgeschlossenen Menge stetig sind. J. reine angew. Math. 145: 9–14
- Tietze, Heinrich (1923). Beiträge zur allgemeinen Topologie. I. Axiome für verschiedene Fassungen des Umgebungsbegriffs. Math. Annalen 88: 290–312
- Tychonoff, A. [Tikhonov, Andrei Nikolaevich] (1930). Über die topologische Erweiterung von Räumen. Math. Ann. 102: 544–561
- Tychonoff, A. [Tikhonov, Andrei Nikolaevich] (1935). Über einen Funktionenraum. Math. Ann. 111: 762–766
- Urysohn, Paul [Urison, Pavel Samuilovich] (1925). Über die Mächtigkeit der zusammen-hängenden Mengen. Math. Ann. 94: 262–295
- Weierstrass, K. (1885). Über die analytische Darstellbarkeit sogenannter willkürlicher Functionen reeller Argumente. Sitzungsber. königl. preussischen Akad. Wissenschaften 633–639, 789–805. Mathematische Werke, Mayer & Müller, Berlin, 1894–1927, vol. 3, pp. 1–37
- Weil, André (1937). Sur les espaces ‘a structure uniforme et sur la topologie générale. Actualités Scientifiques et Industrielles 551, Paris
- Young, W. H., and Grace Chisholm Young (1906). The Theory of Sets of Points. Cambridge Univ. Press.
Reference Title: References
Reference Type: reference-list
- *Borel, Émile (1895). Sur quelques points de la théorie des fonctions. Ann. Ecole Normale Sup. (Ser. 3) 12: 9–55, = Oeuvres, I (CNRS, Paris, 1972), pp. 239–285
- *Borel, Émile (1898). Leçadons sur la théorie des fonctions. Gauthier-Villars, Paris
- *Borel, Émile (1967). Émile Borel: philosophe et homme d'action. Selected, with a Préface, by Maurice Fréchet. Gauthier-Villars, Paris
- *Borel, Émile (1972). Œuvres, 4 vols. Editions du Centre National de la Recherche Scientifique, Paris
- Caratheodory, Constantin (1918). Vorlesungen über reelle Funktionen. Teubner, Leipzig. 2d ed., 1927
- Dubins, Lester E., and Leonard Jimmie Savage (1965). How to Gamble If You Must. McGraw-Hill, New York
- Fréchet, Maurice (1965). La vie et l'oeuvre d'Émile Borel. L'Enseignement Math., Genève, also published in L'Enseignement Math. (Ser. 2) 11 (1965) 1–97
- Hawkins, Thomas (1970). Lebesgue's Theory of Integration: Its Origins and Development. Univ. Wisconsin Press
- Jordan, Camille (1892). Remarques sur les intégrales définies. J. Math. pures appl. (Ser. 4) 8: 69–99
- Kolmogoroff, Andrei N. [Kolmogorov, A. N.] (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer, Berlin. Published in English as Foundations of the Theory of Probability, 2d ed., ed. Nathan Morrison. Chelsea, New York, 1956
- Lebesgue, Henri (1907). Contribution a l'étude des correspondances de M. Zermelo. Bull. Soc. Math. France 35: 202–212
- von Neumann, John (1940–1941). Lectures on invariant measures. Unpublished lecture notes, Institute for Advanced Study, Princeton
- *Radon, Johann (1913). Theorie und Anwendungen der absolut additiven Mengenfunktionen. Wien Akad. Sitzungsber. 122: 1295–1438
- Segal, Irving Ezra (1951). Equivalences of measure spaces. Amer. J. Math. 73: 275–313
- Solovay, Robert M. (1970). A model of set-theory in which every set of reals is Lebesgue measurable. Ann. Math. (Ser. 2) 92: 1–56
- Stieltjes, Thomas Jan (1894). Recherches sur les fractions continues. Ann. Fac. Sci. Toulouse (Ser. 1) 8: 1–122 and 9 (1895): 1–47, = Oeuvres complètes, II (Nordhoff, Groningen, 1918), pp. 402–566
- van Vleck, Edward B. (1908). On non-measurable sets of points with an example. Trans. Amer. Math. Soc. 9: 237–244
- *Vitali, Giuseppe (1905). Sul problema della misura dei gruppi di punti di una retta. Gamberini e Parmeggiani, Bologna
Reference Title: References
Reference Type: reference-list
- Alexits, G. von (1930). Über die Erweiterung einer Baireschen Funktion. Fund. Math. 15: 51–56
- Bledsoe, W. W., and Anthony P. Morse (1955). Product measures. Trans. Amer. Math. Soc. 79: 173–215
- Daniell, Percy J. (1917–1918). A general form of integral. Ann. Math. 19: 279–294
- Dudley, R. M. (1971). On measurability over product spaces. Bull. Amer. Math. Soc. 77: 271–274
- Fatou, Pierre Joseph Louis (1906). Séries trigonométriques et séries de Taylor. Acta Math. 30: 335–400
- Friedman, Harvey (1980). A consistent Fubini-Tonelli theorem for nonmeasurable functions. Illinois J. Math. 24: 390–395
- *Fubini, Guido (1907). Sugli integrali multipli. Rendiconti Accad. Nazionale dei Lincei (Rome) (Ser. 5) 16: 608–614
- Halmos, Paul R. (1950). Measure Theory. Van Nostrand, Princeton. Repr. Springer, New York (1974)
- Hausdorff, Felix (1914) (see references to Chapter 1)
- Hawkins, T. (1970). Lebesgue's Theory of Integration, Its Origins and Development. University of Wisconsin Press
- Hörmander, Lars (1983). The Analysis of Linear Partial Differential Operators, I. Springer, Berlin
- Kuratowski, C. [Kazimierz] (1933). Sur les théorèmes topologiques de la théorie des fonctions de variables réelles. Comptes Rendus Acad. Sci. Paris 197: 19–20
- Kuratowski, C. [Kazimierz] (1966). Topology, vol. 1. Academic Press, New York
- Lebesgue, Henri (1902). Intégrale, longueur, aire (thèse, Univ. Paris). Annali Mat. pura e appl. (Ser. 3) 7: 231–359. Also in Lebesgue (1972–1973) 2, pp. 11–154
- Lebesgue, Henri(1904). Leçcons sur l'intégration et la recherche des fonctions primitives. Paris
- Lebesgue, Henri(1910). Sur l'intégration des fonctions discontinues. Ann. Scient. Ecole Normale Sup. (Ser. 3) 27: 361–450. Also in Lebesgue (1972–1973), 2, pp. 185–274
- Lebesgue, Henri(1972–1973). Oeuvres scientifiques. 5 vols. L'Enseignement Math., Inst. Math., Univ. Genève
- Lehmann, Erich (1959). Testing Statistical Hypotheses. 2d ed. Wiley, New York (1986)
- Levi, Beppo (1906). Sopra l'integrazione delle serie. Rend. Istituto Lombardo di Sci. e Lett. (Ser. 2) 39: 775–780
- May, Kenneth O. (1966). Biographical sketch of Henri Lebesgue. In Lebesgue, H., Measure and the Integral, Ed. K. O. May, Holden-Day, San Francisco, transl. from La Mesure des grandeurs, Enseignement Math 31–34 (1933–1936), repub. as a Monographie (1956)
- Medvedev, F. A. (1975). The work of Henri Lebesgue on the theory of functions (on the occasion of his centenary). Russian Math. Surveys 30, no. 4: 179–191. Transl. from Uspekhi Mat. Nauk 30, no. 4: 227–238
- Nathan, Henry (1971). Fatou, Pierre Joseph Louis. In Dictionary of Scientific Biography, 4, pp. 547–548. Scribner's, New York
- Rudin, Walter (1976). Principles of Mathematical Analysis. 3d ed. McGraw-Hill, New York
- Saks, Stanisław (1937). Theory of the Integral. 2d ed. English transl. by L. C. Young. Hafner, New York. Repr. corrected Dover, New York (1964)
- Schwartz, Laurent (1966). Théorie des Distributions. 2d ed. Hermann, Paris
- Shortt, R. M. (1983). The extension of measurable functions. Proc. Amer. Math. Soc. 87: 444–446
- Sierpiński, Wacław (1920). Sur un problème concernant les ensembles measurables superficiellement. Fundamenta Math. 1: 112–115
- Sierpiński, Wacław(1930). Sur l'extension des fonctions de Baire définies sur les ensembles linéaires quelconques. Fund. Math. 16: 81–89
- Stigler, Stephen M. (1973). Simon Newcomb, Percy Daniell, and the history of robust estimation 1885–1920. J. Amer. Statist. Assoc. 68: 872–879
- Stone, Marshall Harvey (1948). Notes on integration, II. Proc. Nat. Acad. Sci. USA 34: 447–455
- Tonelli, Leonida (1909). Sull'integrazione per parti. Rendiconti Accad. Nazionale dei Lincei (Ser. 5) 18: 246–253. Reprinted in Tonelli, L., Opere Scelte (1960), 1, pp. 156–165. Edizioni Cremonese, Rome
- *Vitali, Giuseppe (1904–05). Sulle funzioni integrali. Atti Accad. Sci. Torino 40: 1021–1034
- *Vitali, Giuseppe(1907). Sull'integrazione per serie. Rend. Circolo Mat. Palermo 23: 137–155
- Zaanen, Adriaan C. (1958). Introduction to the Theory of Integration. North-Holland, Amsterdam
Reference Title: References
Reference Type: reference-list
- Banach, Stefan (1922). Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales. Fundamenta Math. 3: 133–181
- Banach, Stefan (1932). Théorie des operations linéaires. Monografje Matematyczne, Warsaw. 2d ed. (posth.), Chelsea, New York, 1963
- Bell, W. C., and Hagood, J. W. (1981). The necessity of sigma-finiteness in the Radon-Nikodym theorem. Mathematika 28: 99–101
- *Bessel, Friedrich Wilhelm (1875). Abhandlungen. Ed. Rudolf Engelmann. 3 vols. Leipzig
- Buck, R. Creighton (1980). Sherlock Holmes in Babylon. Amer. Math. Monthly 87: 335–345
- *Bunyakovsky, Viktor Yakovlevich (1859). Sur quelques inégalités concernant les intégrales ordinaires et les intégrales aux différences finies. Mémoires de l'Acad. de St.-Petersbourg (Ser. 7) 1, no. 9
- Cauchy, Augustin Louis (1821). Cours d'analyse de l'école Royale Polytechnique (Paris). Also in Oeuvres complètes d'Augustin Cauchy (Ser. 2) 3. Gauthier-Villars, Paris (1897)
- Daniell, Percy J. (1920). Stieltjes derivatives. Bull. Amer. Math. Soc. 26: 444–448
- Dixmier, Jacques (1953). Sur les bases orthonormales dans les espaces préhilbertiens. Acta Sci. Math. Szeged 15: 29–30
- Euler, Leonhard (1755). Institutiones calculi differentialis. Acad. Imp. Sci. Petropolitanae, St. Petersburg; also in Opera Omnia (Ser. 1) 10
- Fatou, Pierre (1906). Séries trigonométriques et séries de Taylor. Acta Math. 30: 335–400
- Fischer, Ernst (1907). Sur la convergence en moyenne. Comptes Rendus Acad. Sci. Paris 144: 1022–1024
- Fréchet, Maurice (1907). Sur les ensembles de fonctions et les opérations linéaires. Comptes Rendus Acad. Sci. Paris 144: 1414–1416
- Fricke, Walter (1970). Bessel, Friedrich Wilhelm. Dictionary of Scientific Biography, 2, pp. 97–102
- *Gram, Jørgen Pedersen (1879). Om Räkkeudviklinger, bestemte ved Hjälp of de mindste Kvadraters Methode (Doctordissertation). Höst, Copenhagen
- *Gram, Jørgen Pedersen (1883). Uber die Entwickelung reeller Functionen in Reihen mittelst der Methode der Kleinsten Quadrate. Journal f. reine u. angew. Math. 94: 41–73
- Hahn, Hans (1921). Theorie der reellen Funktionen, “I. Band.” Julius Springer, Berlin
- Hahn, Hans (posth.) and Arthur Rosenthal (1948). Set Functions. Univ. New Mexico Press
- Hardy, Godfrey Harold, John Edensor Littlewood, and George Polya (1952). Inequalities. 2d ed. Cambridge Univ. Press. Repr. 1967
- Haupt, O. (1960). Arthur Rosenthal (in German). Jahresb. deutsche Math.-Vereinig. 63: 89–96
- Hilbert, David (1904–1910). Grundzüge einer allgemeinen Theorie der linearen Integral-gleichungen. Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. 1904: 49–91, 213–259; 1905: 307–338; 1906: 157–227, 439–480; 1910: 355–417. Also published as a book by Teubner, Leipzig, 1912, repr. Chelsea, New York. 1952
- Hölder, Otto (1889). Über einen Mittelwerthssatz. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. 1889: 38–47
- Hurwitz, A. (1903). Über die Fourierschen Konstanten integrierbarer Funktionen. Math. Annalen 57: 425–446
- Jordan, Camille (1881). Sur la série de Fourier. Comptes Rendus Acad. Sci. Paris 92: 228–230. Also in Jordan (1961–1964), 4, pp. 393–395
- Jordan, Camille (1961–1964). Oeuvres de Camille Jordan. J. Dieudonné and R. Garnier, eds. 4 vols. Gauthier-Villars, Paris
- Lebesgue, Henri (1910). Sur l'intégration des fonctions discontinues. Ann. Scient. Ecole Normale Sup. (Ser. 3) 27: 361–450. Also in Lebesgue (1972–1973) 2, pp. 185–274
- Lebesgue, Henri (1972–1973). Oeuvres scientifiques. 5 vols. L'Enseignement Mathématique. Institut de Mathématique, Univ. Genève
- Levi, Beppo (1906). Sul principio de Dirichlet. Rendiconti Circ. Mat. Palermo 22: 293–360
- Minkowski, Hermann (1907). Diophantische Approximationen. Teubner, Leipzig
- Minkowski, Hermann (1973, posth.). Briefe an David Hilbert. Ed. Lily Rüdenberg and Hans Zassenhaus. Springer, Berlin
- Neugebauer, Otto (1935). Mathematische Keilschrift-Texte. 2 vols. Springer, Berlin
- Neugebauer, Otto (1957). The Exact Sciences in Antiquity. 2d ed. Brown Univ. Press. Repr. Dover, New York (1969)
- von Neumann, John [Johann] (1940). On rings of operators, III. Ann. Math. 41: 94–161
- Nikodym, Otton Martin (1930). Sur une généralisation des mesures de M. J. Radon. Fundamenta Math. 15: 131–179
- *Parseval des Chênes, Marc-Antoine (1799). Mémoire sur les séries et sur l'intégration complète d'une équation aux différences partielles linéaires du second ordre, à coefficiens constans. Mémoires présentés à l'Institut des Sciences, Lettres et Arts, par divers savans, et lus dans ses assemblées. Sciences math. et phys. (savans étrangers) 1 (1806): 638–648
- *Parseval des Chênes, Marc-Antoine (1801). Intégration générale et complète des équations de la propagation du son, l'air étant considéré avec ses trois dimensions. Ibid., pp. 379–398
- *Radon, Johann (1913). Theorie und Anwendungen der absolut additiven Mengenfunktionen. Sitzungsber. Akad. Wiss. Wien Abt. IIa: 1295–1438
- Riesz, Frédéric [Frigyes] (1906). Sur les ensembles de fonctions. Comptes Rendus Acad. Sci. Paris 143: 738–741
- Riesz, Frédéric [Frigyes] (1907a). Sur les systèmes orthogonaux de fonctions. Comptes Rendus Acad. Sci. Paris 144: 615–619
- Riesz, Frédéric [Frigyes] (1907b). Sur une espèce de géométrie analytique des fonctions sommables. Comptes Rendus Acad. Sci. Paris 144: 1409–1411
- Riesz, Frédéric [Frigyes] (1909). Sur les suites de fonctions mesurables. Comptes Rendus Acad. Sci. Paris 148: 1303–1305
- Riesz, Frédéric [Frigyes] (1910). Untersuchungen über Systeme integrierbarer Funktionen. Math. Annalen 69: 449–497
- Riesz, Frédéric [Frigyes] (1934). Zur Theorie des Hilbertschen Raumes. Acta Sci. Math. Szeged 7: 34–38
- Rogers, Leonard James (1888). An extension of a certain theorem in inequalities. Messenger of Math. 17: 145–150
- Rüdenberg, Lily (1973). Erinnerungen an H. Minkowski. In Minkowski (1973), pp. 9–16
- Schmidt, Erhard (1907). Zur Theorie der linearen und nichtlinearen Integralgleichungen. I. Teil: Entwicklung willkürlicher Funktionen nach Systemen vorgeschriebener. Math. Annalen 63: 433–476
- Schmidt, Erhard (1907). Auflösung der allgemeinen linearen Integralgleichung. Math. Annalen 64: 161–174
- Schmidt, Erhard (1908). Über die Auflösung linearer Gleichungen mit unendlich vielen Unbekannten. Rend. Circ. Mat. Palermo 25: 53–77
- *Schwarz, Hermann Amandus (1885). Über ein die Flächen kleinsten Flächeninhalts betreffendes Problem der Variationsrechnung. Acta Soc. Scient. Fenn. 15: 315–362
- Schweder, Tore (1980). Scandinavian statistics, some early lines of development. Scand. J. Statist 7: 113–129
- Siegmund-Schultze, Reinhard (1982). Die Anfänge der Funktionalanalysis und ihr Platz im Umwälzungsprozess der Mathematik um 1900. Arch. Hist. Exact Sci. 26: 13–71
- Stanley, Richard P. (1971). Theory and application of plane partitions. Studies in Applied Math. 50: 167–188
- Steinhaus, Hugo (1961). Stefan Banach, 1892–1945. Scripta Math. 26: 93–100
- van der Waerden, Bartel Leendert (1939). Nachruf auf Otto Hölder. Math. Ann. 116: 157–165
- Watson, George Neville (1944). A Treatise on the Theory of Bessel Functions, 2d ed. Cambridge Univ. Press, repr. 1966; 1st ed., 1922
- Wiener, Norbert (1922). Limit in terms of continuous transformation. Bull. Soc. Math. France 50: 119–134
Reference Title: References
Reference Type: reference-list
- Banach, Stefan (1929). Sur les fonctionelles linéaires I, II. Studia Math. 1: 211–216, 223–239
- Banach, Stefan(1931). Über metrische Gruppen. Studia Math. 3: 101–113
- Banach, Stefan(1932). Théorie des Opérations Linéaires. Monografje Matematyczne I, Warsaw
- Banach, Stefanand Hugo Steinhaus (1927). Sur le principe de la condensation de singularités. Fund. Math. 9: 50–61
- Bonnesen, Tommy, and Werner Fenchel (1934). Theorie der konvexen Körper. Springer, Berlin. Repub. Chelsea, New York, 1948
- *Brunn, Hermann (1887). Über Ovale and Eiflächen. Inauguraldissertation, Univ. München
- *Brunn, Hermann(1889). Über Kurven ohne Wendepunkte. Habilitationsschrift, Univ. München
- *Brunn, Hermann (1910). Zur Theorie der Eigebiete. Arch. Math. Phys. (Ser. 3) 17: 289–300
- Dieudonné, Jean (1941). Sur le théorème de Hahn-Banach. Rev. Sci. 79: 642–643
- Dieudonné, Jean(1943). Sur la séparation des ensembles convexes dans un espace de Banach. Rev. Sci. 81: 277–278
- Dunford, Nelson (1981). [Response]. Amer. Math. Soc. Notices 28: 509–510
- Dunford, Nelsonand Jacob T. Schwartz, with the assistance of William G. Badé and Robert G. Bartle (1958). Linear Operators: Part I, General Theory. Interscience, New York
- Eidelheit, Maks (1936). Zur Theorie der konvexen Mengen in linearen normierten Räumen. Studia Math. 6: 104–111
- Hadwiger, H., and D. Ohmann (1956). Brunn-Minkowskischer Satz und Isoperimetrie. Math. Zeitschr. 66: 1–8
- Hahn, Hans (1922). Über Folgen linearer Operationen. Monatsh. für Math. und Physik 32: 3–88
- Hahn, Hans (1927). Über lineare Gleichungssyteme in linearen Räumen. J. für die reine und angew. Math. 157: 214–229
- Hardy, Godfrey Harold, John Edensor Littlewood, and George Polya (1934). Inequalities. Cambridge University Press 2d ed., 1952, repr. 1967
- Hildebrandt, T. H. (1923). On uniform limitedness of sets of functional operations. Bull. Amer. Math. Soc. 29: 309–315
- Hörmander, Lars (1964). Linear partial differential operators. Springer, Berlin
- Jensen, Johan Ludvig William Valdemar (1906). Sur les fonctions convexes et les inégalites entre les valeurs moyennes. Acta Math. 30: 175–193
- Kelley, John L., Isaac Namioka, and eight co-authors (1963). Linear Topological Spaces. Van Nostrand, Princeton. Repr. Springer, New York (1976)
- Kirszbraun, M. D. (1934). Über die zusammenziehenden und Lipschitzschen Transformationen. Fund. Math. 22: 77–108
- Lipschitz, R. O. S. (1864). Recherches sur le développement en séries trigonométriques des fonctions arbitraires et principalement de celles qui, dans un intervalle fini, admettent une infinité de maxima et de minima (in Latin). J. reine angew. Math. 63: 296–308; French transl. in Acta Math. 36 (1913): 281–295
- McShane, Edward J. (1934). Extension of range of functions. Bull. Amer. Math. Soc. 40: 837–842
- Minkowski, Hermann (1897). Allgemeine Lehrsätze über die konvexen Polyeder. Nachr. Ges. Wiss. Göttingen Math. Phys. Kl. 1897: 198–219; Gesammelte Abhandlungen, 2 (Leipzig and Berlin, 1911, repr. Chelsea, New York, 1967), pp. 103–121
- Minkowski, Hermann(1901). Sur les surfaces convexes fermées. C. R. Acad. Sci. Paris 132: 21–24; Gesammelte Abhandlungen, 2, pp. 128–130
- Minkowski, Hermann(1910). Geometrie der Zahlen. Teubner; Leipzig; repr. Chelsea, New York, 1953
- Minkowski, Hermann (1911, posth.). Theorie der konvexen Körper, insbesondere Begründung des Oberflächenbegriffs. Gesammelte Abhandlungen, 2, pp. 131–229
- Minty, George J. (1970). On the extension of Lipschitz, Lipschitz-Hölder continuous, and monotone functions. Bull. Amer. Math. Soc. 76: 334–339
- Riesz, F. (1910). Untersuchungen über Systeme integrierbarer Funktionen. Math. Annalen 69: 449–497
- Roberts, Arthur Wayne, and Dale E. Varberg (1973). Convex Functions. Academic Press, New York
- Rockafellar, R. Tyrrell (1970). Convex Analysis. Princeton University Press
- Schauder, Juliusz (1930). Über die Umkehrung linearer, stetiger Funktionaloperationen. Studia Math. 2: 1–6
Reference Title: References
Reference Type: reference-list
- *Ambrose, Warren (1946). Lectures on topological groups (unpublished). Ann Arbor
- *du Bois-Reymond, P. (1876). Untersuchungen über die Convergenz und Divergenz der Fourierschen Darstellungsformeln. Abh. Akad. München 12: 1–103
- Carleson, Lennart (1966). On convergence and growth of partial sums of Fourier series. Acta Math. 116: 135–157
- Egoroff, Dmitri (1911). Sur les suites de fonctions mesurables. C. R. Acad. Sci. Paris 152: 244–246
- Fefferman, Charles (1971). On the convergence of multiple Fourier series. Bull. Amer. Math. Soc. 77: 744–745
- Fourier, Jean Baptiste Joseph (1822). Théorie analytique de la chaleur. F. Didot, Paris
- *Fourier, Jean Baptiste Joseph (1824). Théorie du mouvement de la chaleur dans les corps solides. Mémoires de l'Acad. Royale des Sciences 4 (1819–1820; publ. 1824): 185–555
- *Fourier, Jean Baptiste Joseph (1826). Suite du mémoire intitulé: “Théorie du mouvement de la chaleur dans les corps solides.” Mémoires de l'Acad. Royale des Sciences 5 (1821–1822; publ. 1826): 153–246; Oeuvres de Fourier, 2, pp. 1–94
- Fourier, Jean Baptiste Joseph (1888–1890, posth.) Oeuvres. Ed. G. Darboux. Gauthier-Villars, Paris
- Garling, David J. H. (1986). Another ‘short’ proof of the Riesz representation theorem. Math. Proc. Camb. Phil. Soc. 99: 261–262
- Grattan-Guinness, Ivor (1972). Joseph Fourier, 1768–1830. MIT Press, Cambridge, Mass
- Grebogi, Celso, Edward Ott, and James A. Yorke (1987). Chaos, strange attractors, and fractal basin boundaries in nonlinear dynamics. Science 238: 632–638
- Halmos, Paul (1950). Measure Theory. Van Nostrand, Princeton
- Herivel, John (1975). Joseph Fourier: The Man and the Physicist. Clarendon Press, Oxford
- Hunt, R. A. (1968). On the convergence of Fourier series. In Orthogonal Expansions and Their Continuous Analogues, pp. 235–255. Southern Illinois Univ. Press
- *Kakutani, Shizuo, and Kunihiko Kodaira (1944). Über das Haarsche Mass in der lokal bikompakten Gruppe. Proc. Imp. Acad. Tokyo 20: 444–450
- *Kodaira, Kunihiko (1941). Über die Beziehung zwischen den Massen und Topologien in einer Gruppe. Proc. Math.-Phys. Soc. Japan 23: 67–119
- Kolmogoroff, Andrei N. [Kolmogorov, A. N.] (1923). Une série de Fourier-Lebesgue divergente presque partout. Fund. Math. 4: 324–328
- Kolmogoroff, Andrei N. [Kolmogorov, A. N.] (1926). Une série de Fourier-Lebesgue divergente partout. C. R. Acad. Sci. Paris 183: 1327–1328
- Lebesgue, Henri Léon (1904). Leçons sur l'intégration et la recherche des fonctions primitives, Paris. 2d ed., 1928. Repr. in Oeuvres Scientifiques 2, pp. 111–154
- Lebesgue, Henri Léon (1910). Sur l'intégration des fonctions discontinues. Ann. Ecole Norm. Sup. (Ser. 3) 27: 361–450. Repr. in Oeuvres Scientifiques 2, pp. 185–274
- Lusin, Nikolai (1912). Sur les propriétés des fonctions mesurables. C. R. Acad. Sci. Paris 154: 1688–1690
- von Neumann, Johann (1932). Einige Sätze üuber messbare Abbildungen. Ann. Math. 33: 574–586, and Collected Works [1961, below], 2, no. 16, p. 297
- von Neumann, Johann (1940–1941). Lectures on invariant measures. Notes by Paul R. Halmos. Unpublished. Institute for Advanced Study, Princeton
- von Neumann, Johann (1961–1963). Collected Works. Ed. A. H. Taub. Pergamon Press, London
- Oxtoby, John C., and Stanislaw M. Ulam (1939). On the existence of a measure invariant under a transformation. Ann. Math. (Ser. 2) 40: 560–566
- Paplauskas, A. B. (1971). Egorov, Dimitry Fedorovich. Dictionary of Scientific Biography, 4, pp. 287–288
- Ravetz, Jerome R., and Ivor Grattan-Guinness (1972). Fourier, Jean Baptiste Joseph. Dictionary of Scientific Biography 5, pp. 93–99
- Riesz, Frigyes [Frédéric] (1909). Sur les opérations fonctionnelles linéaires. Comptes Rendus Acad. Sci. Paris 149: 974–977
- *Riesz, Frigyes [Frédéric] (1914). Démonstration nouvelle d'un théorème concernant les opérations. Ann. Ecole Normale Sup. (Ser. 3) 31: 9–14
- *Riesz, Frigyes [Frédéric] (1930–1932). Sur l'existence de la dérivée des fonctions monotones et sur quelques problèmes qui s'y rattachent. Acta Sci. Math. Szeged 5: 208–221
- Riesz, Frigyes [Frédéric] and Béla Szökefalvi-Nagy (1953). Functional Analysis. Ungar, New York (1955). Transl. L. F. Boron from 2d French ed., Leçons d'analyse fonctionelle. 5th French ed., Gauthier-Villars, Paris (1968)
- Rudin, Walter (1966, 1974, 1987). Real and Complex Analysis. 1st, 2d and 3d eds. McGraw-Hill, New York
- Rudin, Walter (1976). Principles of Mathematical Analysis. 3d ed. McGraw-Hill, New York
- Saks, Stanisłash aw (1937). Theory of the Integral. 2d ed. Monografie Matematyczne, Warsaw; English transl. L. C. Young. Hafner, New York. Repr. Dover, New York (1964)
- Schaerf, H. M. (1947). On the continuity of measurable functions in neighborhood spaces. Portugal. Math. 6: 33–44
- Schaerf, H. M. (1948). On the continuity of measurable functions in neighborhood spaces II. Ibid. 7: 91–92
- Ulam, Stanislaw Marcin (1976). Adventures of a Mathematician. Scribner's, New York
- *Vitali, Giuseppe (1904–05). Sulle funzioni integrali. Atti Accad. Sci. Torino 40: 1021–1034
- *Vitali, Giuseppe (1908). Sui gruppi di punti e sulle funzioni di variabili reali. Ibid. 43: 75–92
- Zakon, Elias (1965). On “essentially metrizable” spaces and on measurable functions with values in such spaces. Trans. Amer. Math. Soc. 119: 443–453
- Zygmund, Antoni (1959). Trigonometric Series. 2 vols. 2d ed. Cambridge University Press
Reference Title: References
Reference Type: reference-list
- Andersen, Eric Sparre, and Borge Jessen (1946). Some limit theorems on integrals in an abstract set. Danske Vid. Selsk. Mat.-Fys. Medd. 22, no. 14. 29 pp.
- Andersen, Eric Sparre, and Borge Jessen (1948). On the introduction of measures in infinite product sets. Danske Vid. Selsk. Mat.-Fys. Medd. 25, no. 4. 8 pp.
- Banach, Stefan (1923). Sur le problème de la mesure. Fundamenta Mathematicae 4: 7–33
- Barone, Jack, and Albert Novikoff (1978). A history of the axiomatic formulation of probability from Borel to Kolmogorov: Part I. Arch. Hist. Exact Sci. 18: 123-190
- Benzi, Margherita (1988). A “neoclassical probability theorist:” Francesco Paolo Cantelli (in Italian). Historia Math. 15: 53–72
- Bernoulli, Jakob (1713, posth.). Ars Conjectandi. Thurnisiorum, Basel. Repr. in Die Werke von Jakob Bernoulli 3 (1975), pp. 107–286. Birkhäuser, Basel
- Bienaymé, Irenée-Jules (1853). Considérations a l'appui de la découverte de Laplace sur la loi de probabilité dans la méthode des moindres carrés. C.R. Acad. Sci. Paris 37: 309–324. Repr. in J. math. pures appl. (Ser. 2) 12 (1867): 158–276
- Billingsley, Patrick (1965). Ergodic Theory and Information. Wiley, New York
- Bingham, N. H. (2000). Studies in the history of probability and statistics XⅬVI. Measure into probability: From Lebesgue to Kolmogorov. Biometrika 87: 145–156
- Birkhoff, George D. (1932). Proof of the ergodic theorem. Proc. Nat. Acad. Sci. USA 17: 656–660
- Boltzmann, Ludwig (1887). Ueber die mechanischen Analogien des zweiten Hauptsatzes der Thermodynamik. J. für die reine und angew. Math. 100: 201-212
- Borel, Émile (1903). Contribution à 1'analyse arithmétique du continu. J. math. pures appl. (Ser. 2) 9: 329–375
- Borel, Émile (1909). Les probabilités dénombrables et leurs applications arithmétiques. Rendiconti Circolo Mat. Palermo 27: 247–271
- Brunel, Antoine (1963). Sur un lemme ergodique voisin du lemme de E. Hopf, et sur une de ses applications. C. R. Acad. Sci. Paris 256: 5481–5484
- Brush, Stephen G. (1976). The Kind of Motion We Call Heat. 2 vols. North-Holland, Amsterdam
- *Buffon, Georges L. L. (1733). Histoire de l' Académie. Paris
- *Buffon, Georges L. L. (1778). X Essai d'Arithmétique Morale. In Histoire Naturelle, pp. 67–216. Paris
- *Cantelli, Francesco Paolo (1917a). Sulla probabilità come limite della frequenza. Accad. Lincei, Roma, Cl. Sci. Fis., Mat., Nat., Rendiconti (Ser. 5) 26: 39–45
- *Cantelli, Francesco Paolo (1917b). Su due applicazione di un teorema di G. Boole alla statistica matematica. Ibid., pp. 295–302
- Chacon, Rafael V. (1961). On the ergodic theorem without assumption of positivity. Bull. Amer. Math. Soc. 67: 186–190
- Chacon, Rafael V. and Donald S. Ornstein (1960). A general ergodic theorem. Illinois J. Math. 4: 153–160
- Chebyshev, Pafnuti Lvovich (1867). Des valeurs moyennes. J. math. pures appl. 12 (1867): 177–184. Transl. from Mat. Sbornik 2 (1867): 1–9. Repr. in Oeuvres de P. L. Tchebychef 1, pp. 687–694. Acad. Sci. St. Petersburg (1899–1907)
- Chung, Kai Lai (1974). A Course in Probability Theory. 2d ed. Academic Press, New York
- Cohn, Harry (1972). On the Borel-Cantelli Lemma. Israel J. Math. 12: 11–16
- Daniell, Percy J. (1919). Integrals in an infinite number of dimensions. Ann. Math. 20: 281–288
- Day, Mahlon M. (1942). Ergodic theorems for Abelian semi-groups. Trans. Amer. Math. Soc. 51: 399–412
- Dubins, Lester E., and Leonard Jimmie Savage (1965). How to Gamble If You Must; Inequalities for Stochastic Processes. McGraw-Hill, New York
- Dugac, P. (1976). Notes et documents sur la vie et l'oeuvre de René Baire. Arch. Hist. Exact Sci. 15: 297–383
- Dunford, Nelson, and Jacob T. Schwartz (1956). Convergence almost everywhere of operator averages. J. Rat. Mech. Anal. (Indiana Univ.) 5: 129–178
- Ehrenfeucht, Andrzej, and Marek Fisz (1960). A necessary and sufficient condition for the validity of the weak law of large numbers. Bull. Acad. Polon. Sci. Ser. Math. Astron. Phys. 8: 583–585
- *Erdös, Paul, and Alfréd Rényi (1959). On Cantor's series with divergent Σ 1\qn. Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 2: 93–109
- Etemadi, Nasrollah (1981). An elementary proof of the strong law of large numbers. Z. Wahrsch. verw. Geb. 55: 119–122
- Feller, William (1968). An Introduction to Probability Theory and Its Applications. Vol. 1, 3d ed. Wiley, New York
- Garsia, Adriano M. (1965). A simple proof of E. Hopf's maximal ergodic theorem. J. Math. and Mech. (Indiana Univ.) 14: 381–382
- Garsia, Adriano M. (1967). More about the maximal ergodic lemma of Brunel. Proc. Nat. Acad. Sci. USA 57: 21–24
- Gnedenko, Boris V. (1973). Andrei Nikolaevich Kolmogorov (On his 70th birthday). Russian Math. Surveys 28, no. 5: 5–17. Transl. from Uspekhi Mat. Nauk 28, no. 5: 5–15
- Gnedenko, Boris V. and Andrei Nikolaevich Kolmogorov (1949). Limit Distributions for Sums of Independent Random Variables. Translated, annotated, and revised by Kai Lai Chung, with appendices by Joseph L. Doob and Pao Lo Hsu. Addison-Wesley, Reading, Mass. 1st ed. 1954, 2d ed. 1968
- Gnedenko, Boris V. and N. V. Smirnov (1963). On the work of A. N. Kolmogorov in the theory of probability. Theory Probability Appls. 8: 157–164
- Godwin, H. J. (1955). On generalizations of Tchebychef's inequality. J. Amer. Statist. Assoc. 50: 923–945
- Godwin, H. J. (1964). Inequalities on Distribution Functions. Griffin, London
- Greenleaf, Frederick P. (1969). Invariant Means on Topological Groups and their Applications. Van Nostrand, New York
- ter Haar, D. (1954). Elements of Statistical Mechanics. Rinehart, New York
- Halmos, Paul R. (1953). Lectures on Ergodic Theory. Math. Soc. of Japan, Tokyo
- Hausdorff, Felix (1914). Grundzüge der Mengenlehre, 1st ed. Von Veit, Leipzig, repr. Chelsea, New York, 1949
- Hewitt, Edwin, and Leonard Jimmie Savage (1955). Symmetric measures on Cartesian products. Trans. Amer. Math. Soc. 80: 470–501
- Heyde, Christopher C., and Eugene Seneta (1977). I. J. Bienaymé: Statistical Theory Anticipated. Springer, New York
- Hopf, Eberhard (1937). Ergodentheorie. Springer, Berlin
- Hopf, Eberhard (1954). The general temporally discrete Markoff process. J. Rat. Mech. Anal. (Indiana Univ.) 3: 13–45
- Ionescu Tulcea, Cassius (1949–1950). Mesures dans les espaces produits. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (Ser. 8) 7: 208–211
- Jacobs, Konrad (1963). Lecture Notes on Ergodic Theory. Aarhus Universitet, Matematisk Institut
- Jessen, Borge (1939). Abstrakt Maalog Integralteori 4. Mat. Tidsskrift (B) 1939, pp. 7–21
- Jordan, Kàroly (1972). Chapters on the Classical Calculus of Probability. Akadémiai Kiadó, Budapest
- Kakutani, Shizuo (1943). Notes on infinite product measures, I. Proc. Imp. Acad. Tokyo (became Japan Academy Proceedings)19: 148–151
- Khinchin, A. Ya. (1933). Zu Birkhoffs Lösung des Ergodenproblems. Math. Ann. 107: 485–488
- Kolmogorov, Andrei Nikolaevich (1929a). Bemerkungen zu meiner Arbeit “Über die Summen zufälliger Grössen.” Math. Ann. 102: 484–488
- Kolmogorov, Andrei Nikolaevich (1929b). The general theory of measure and the calculus of probability (in Russian). In Coll. Works, Math. Sect. (Communist Acad., Sect. Nat. Exact Sci.) 1, 8–21. Izd. Komm. Akad., Moscow. Repr. in Kolmogorov (1986), pp. 48–58
- Kolmogorov, Andrei Nikolaevich (1930). Sur la loi forte des grandes nombres. Comptes Rendus Acad. Sci. Paris 191: 910–912
- Kolmogorov, Andrei Nikolaevich (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung, Ergebnisse der Math., Springer, Berlin. English transl. Foundations of the Theory of Probability, Chelsea, New York, 1956
- Kolmogorov, Andrei Nikolaevich (1986). Probability Theory and Mathematical Statistics [in Russian; selected works], ed. Yu. V. Prohorov. Nauka, Moscow
- Łomnicki, Z., and Stanisław Ulam (1934). Sur la théorie de la mesure dans les espaces combinatoires et son application au calcul des probabilités: I. Variables indépendantes. Fund. Math. 23: 237–278
- *Markov, Andrei Andreevich (1899). The law of large numbers and the method of least squares (in Russian). Izv. Fiz.-Mat. Obshch. Kazan Univ. (Ser. 2) 8: 110–128
- Móri, T. F., and G. J. Székely (1983). On the Erdös-Rényi generalization of the Borel-Cantelli lemma. Stud. Sci. Math. Hungar. 18: 173–182
- von Neumann, Johann (1929). Zur allgemeinen Theorie des Masses. Fund. Math. 13: 73–116
- von Neumann, Johann (1935). Functional Operators. Mimeographed lecture notes. Institute for Advanced Study, Princeton, N. J. Published in Ann. Math. Studies no. 21, Functional Operators, vol. I, Measures and Integrals. Princeton University Press, 1950
- Notices, Amer. Math. Soc. 28 (1981, p. 84; unsigned). 1980 Wolf Prize
- Ornstein, Donald S., D. J. Rudolph, and B. Weiss (1982). Equivalence of measure preserving transformations. Amer. Math. Soc. Memoirs 262
- Plancherel, Michel (1912). Sur l'incompatibilité de l'hypothèse ergodique et des équations d'Hamilton. Archives sci. phys. nat. (Ser. 4) 33: 254–255
- Plancherel, Michel (1913). Beweis der Unmöglichkeit ergodischer mechanischer Systeme. Ann. Phys. (Ser. 4) 42: 1061–1063
- Révész, Pal (1968). The Laws of Large Numbers. Academic Press, New York
- Rosenthal, Arthur (1913). Beweis der Unmöglichkeit ergodischer Gassysteme. Ann. Phys. (Ser. 4) 42: 796–806
- Savage, I. Richard (1961). Probability inequalities of the Tchebycheff type. J. Research Nat. Bur. Standards 65B, pp. 211–222
- Seneta, Eugene (1992). On the history of the strong law of large numbers and Boole's inequality. Historia Mathematica 19: 24–39
- Sheynin, O. B. (1968). On the early history of the law of large numbers. Biometrika 55, pp. 459–467
- Shiryayev, A. N. (1989). Kolmogorov: Life and creative activities. Ann. Probab. 17: 866–944
- The Times [London, unsigned] (26 October 1987). Andrei Nikolaevich Kolmogorov: 1903–1987. Repr. in Inst. Math. Statist. Bulletin 16: 324–325
- Ulam, Stanisław (1932). Zum Massbegriffe in Produkträumen. Proc. International Cong. of Mathematicians (Zürich), 2, pp. 118–119
- Yosida, Kosaku, and Shizuo Kakutani (1939). Birkhoff's ergodic theorem and the maximal ergodic theorem. Proc. Imp. Acad. (Tokyo)15: 165–168
- Youschkevitch [Yushkevich], Alexander A. (1974). Markov, Andrei Andreevich. Dictionary of Scientific Biography, 9, pp. 124–130
- Youschkevitch, A. P. (1971). Chebyshev, Pafnuti Lvovich. Dictionary of Scientific Biography, 3, pp. 222–232
Reference Title: References
Reference Type: reference-list
- Alexandroff, A. D. (1940, 1941, 1943). Additive set-functions in abstract spaces. Mat. Sbornik (N. S.) 8: 307–348; 9: 563–628; 13: 169–238
- Alexandroff, P. S., N. I. Akhiezer, B. V. Gnedenko, and A. N. Kolmogorov (1969). Sergei Natanovich Bernstein: Obituary. Russian Math. Surveys 24, no. 3, pp. 169–176. Transl. from Uspekhi Mat. Nauk 24, no. 3, pp. 211–218
- Archibald, R. C. (1926). A rare pamphlet of Moivre and some of his discoveries. Isis 8: 671–676
- Baron, Margaret E. (1976). Todhunter, Isaac. Dictionary of Scientific Biography, 13, 426–428
- Bernstein, Serge [Sergei Natanovich] (1927). Sur l'extension du théorème limite du calcul des probabilités aux sommes de quantités dépendantes. Math. Ann. 97: 1–59
- Bochner, Salomon (1932). Vorlesungen üuber Fouriersche Integrale. Akademische Verlagsges. M. B. H., Leipzig. Repr. Chelsea, New York, 1948
- Breiman, Leo (1968). Probability. Addison-Wesley, Reading, Mass
- Cauchy, Augustin-Louis (1853). Sur les resultats moyens d'observations de même nature, et sur les resultats les plus probables. Comptes Rendus Acad. Sci. Paris 37: 198–206. Sur la probabilité des erreurs qui affectent des resultats moyens d'observations de même nature. Ibid., pp. 264–272. Mémoire sur les resultats moyens d'un très-grand nombre d'observations [Summary]. Ibid., pp. 381–385
- Cramér, Harald (1976). Half a century with probability theory: Some personal recollections. Ann. Probability 4: 509–546
- Daw, R. H., and E. S. Pearson (1972). Studies in the history of probability and statistics, XXX. Abraham De Moivre's 1733 derivation of the normal curve: a bibliographical note. Biometrika 59: 677–680
- Efimov, N. V., V. A. Zalgaller, and A. V. Pogorelov (1962). Alexander Danilovich Alexandrov (On his 50th birthday). Russian Math. Surveys 17, no. 6: 127–133. Transl. from Uspekhi Mat. Nauk 17, no. 6: 171–184
- Fan, Ky (1944). Entfernung zweier zufälligen Grössen und die Konvergenz nach Wahrscheinlichkeit. Math. Zeitschr. 49: 681–683
- Feller, Willy (1935). ÜUber den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung. Math. Zeitschr. 40: 521–559
- Feller, Willy (1968). An Introduction to Probability Theory and Its Applications. Vol. 1, 3d ed. Wiley, New York
- Fréchet, Maurice (1921). Sur divers modes de convergence d'une suite de fonctions d'une variable. Bull. Calcutta Math. Soc. 11: 187–206
- Fréchet, Maurice (1928). Les espaces abstraits … Gauthier-Villars, Paris
- Fréchet, Maurice (1937). Recherches théoriques modernes sur la théorie des probabilités I. Paris
- Gikhman, I. I., A. N. Kolmogorov, and V. S. Korolyuk (1962). Boris Vladimirovich Gnedenko (On his 50th birthday). Russian Math. Surveys 17, no. 4: 105–113. Transl. from Uspekhi Mat. Nauk 17, no. 4: 191–200
- Gnedenko, Boris V., and Andrei N. Kolmogorov (1949). Limit Distributions for Sums of Independent Random Variables. Translated, annotated, and revised by Kai Lai Chung. Addison-Wesley, Reading, Mass., 1954, 2d ed. 1968, with appendices by J. L. Doob and P. L. Hsu
- Hald, Anders (1984). A. de Moivre: “De Mensura Sortis” or “On the measurement of chance.” Transl. with commentary. Internat. Statist. Rev. 52: 229–262
- Hall, Peter (1981). A comedy of errors: The canonical form for a stable characteristic function. Bull. London Math. Soc. 13: 23–27
- Hoffman, Kenneth, and Ray Kunze (1971). Linear Algebra. 2d ed. Prentice-Hall, Englewood Cliffs, N.J
- Khinchin, A. Ya. [Aleksandr Yakovlevich] (1933). Asymptotische Gesetze der Wahrscheinlichkeitsrechnung. Springer, Berlin
- Khinchin, A. Ya. [Aleksandr Yakovlevich], and A. N. Kolmogoroff (1925). Über Konvergenz von Reihen deren Glieder durch den Zufall bestimmt werden. Mat. Sbornik (Recueil Math.) 32: 668–676. Russ. Summary, p. 677
- Khinchin, A. Ya. [Aleksandr Yakovlevich, and P. Lévy (1936). Sur les lois stables. C. R. Acad. Sci. Paris 202: 374–376
- Kolmogoroff, A. N. [Kolmogorov, Andrei Nikolaevich] (1928, 1929). Über die Summen durch den Zufall bestimmter unabhängiger Grössen. Math. Annalen 99: 309–319. Bemerkungen zu meiner Arbeit … Ibid. 102: 484–488
- Laplace, Pierre Simon de (1774). Mémoire sur la probabilité des causes par les événemens. Mémoires de mathématique et de physique présentés a l'Académie royale des sciences, par divers savans & lus dans ses assemblées 6: 621–656. Repr. in Oeuvres complètes de Laplace, 8, 325–366. Transl. into English and included (except an “unrelated” §7, on differential equations) in Stigler (1986, pp. 364–378)
- Laplace, Pierre Simon de (1812). Théorie analytique des probabilités. 3d ed. (1820). Mme Ve Courcier, Paris. Repr. in Oeuvres complètes de Laplace, 7
- Laplace, Pierre Simon de (1886–1912). Oeuvres complètes de Laplace. Gauthier-Villars, Paris
- Lévy, Paul (1922a). Sur le rôle de la loi de Gauss dans la théorie des erreurs. C. R. Acad. Sci. Paris 174: 855–857
- Lévy, Paul (1922b). Sur la loi de Gauss. C. R. Acad. Sci. Paris 174: 1682–1684
- Lévy, Paul (1922c). Sur la détermination des lois de probabilité par leurs fonctions caractéristiques. C. R. Acad. Sci. Paris 175: 854–856
- Lévy, Paul (1924). Théorie des erreurs. La loi de Gauss et les lois exceptionelles. Bull. Soc. Math. France 52: 49–85
- Lévy, Paul (1925). Calcul des probabilités. Gauthier-Villars, Paris
- Lévy, Paul (1935). Propriétés asymptotiques des sommes de variables indépendantes ou enchaînées. J. math. pures appl. (Ser. 9) 14: 347–402
- Lévy, Paul (1937). Théorie de l'addition des variables aléatoires. Gauthier-Villars, Paris. 2d ed. 1954
- Lévy, Paul (1970). Quelques aspects de la pensée d'un mathématicien. Blanchard, Paris
- Lévy, Paul (1973–1980). Oeuvres de Paul Lévy. 6 vols. Gauthier-Villars, Paris
- Lindeberg, J. W. (1922a). Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung. Math. Zeitschr. 15: 211–225
- Lindeberg, J. W. (1922b). Sur la loi de Gauss. C. R. Acad. Sci. Paris 174: 1400–1402
- Loève, Michel (1977). Probability Theory I. 4th ed. Springer, New York
- *Lyapunoff, A. M. (1901). Nouvelle forme du théorème sur la limite des probabilités. Mem. Acad. Sci. St. Petersburg 12, no. 5: 1–24
- de Moivre, Abraham (1711–1712). De Mensura Sortis seu, de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus. Phil. Trans. Roy. Soc. London 27, whole no. 329. Transl. in Hald (1984)
- de Moivre, Abraham (1730). Miscellanea Analytica. London
- de Moivre, Abraham (1733). Approximatio ad Summam Terminorum Binomii (a + b)n in Seriem Expansi. 7 pp. London. Repr. in Archibald (1926)
- de Moivre, Abraham (1756, posth.). The Doctrine of Chances, 3d. ed. London. Repr. F. Case, London, and Chelsea, New York, 1967
- Ottaviani, G. (1939). Sulla teoria astratta del calcolo delle probabilità proposita dal Cantelli. Giorn. Ist. Ital. Attuari 10: 10–40
- Pearson, Karl (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Phil. Mag. (Ser. 5) 50: 157–175
- Pearson, Karl (1924). Historical note on the origin of the normal curve of errors. Biometrika 16: 402–404
- Poisson, Siméon D. (1837). Recherches sur la probabilité des jugements en matière criminelle et en matière civile précédés des règles générales du calcul des probabilités. Bachelier, Paris
- Riesz, F. (1909). Sur les suites de fonctions mesurables. Comptes Rendus Acad. Sci. Paris 148: 1303–1305
- Schneider, Ivo (1968–1969). Der Mathematiker Abraham de Moivre, 1667–1754. Arch. Hist. Exact. Sci. 5: 177–317
- Schweder, Tore (1980). Scandinavian statistics, some early lines of development. Scand. J. Statist. 7: 113–129
- Sheynin, O. B. (1977). S. D. Poisson's work in probability. Arch. Hist. Exact Sci. 18: 245–300
- Stigler, Stephen M. (1986). Laplace's 1774 memoir on inverse probability. Statistical Science 1: 359–378
- Stirling, James (1730). Methodus Differentialis. London
- Todhunter, Isaac (1865). A History of the Mathematical Theory of Probability from the Time of Pascal to That of Laplace. Macmillan, London
Reference Title: References
Reference Type: reference-list
- Andersen, Erik Sparre, and Børge Jessen (1946). Some limit theorems on integrals in an abstract set. Danske. Vid. Selsk. Mat.-Fys. Medd. 22, no. 14. 29 pp
- Andersen, Erik Sparre, and Børge Jessen (1948a). On the introduction of measures in infinite product sets. Danske Vid. Selsk. Mat.-Fys. Medd. 25, no. 4. 8 pp
- Andersen, Erik Sparre, and Børge Jessen (1948b). Some limit theorems on set-functions. Danske Vid. Selsk. Mat.-Fys. Medd. 25, no. 5. 8 pp
- Baez-Duarte, Luis (1968). Another look at the martingale theorem. J. Mathematical Analysis and Appls. 23: 551–557
- Bauer, Heinz (1968). Wahrscheinlichkeitstheorie und Grundzüge der Masstheorie. De Gruyter, Berlin. Publ. in English as Probability Theory and Elements of Measure Theory. Transl. Lisa Rosenblatt. Holt, Rinehart & Winston, New York, 1972
- Blackwell, David, and Lester E. Dubins (1963). A converse to the dominated convergence theorem. Illinois J. Math. 7: 508–514
- Dieudonné, Jean (1948). Sur le théorème de Lebesgue-Nikodym (III). Ann. Inst. Fourier (Grenoble) (Ser. 2) 23: 25–53
- Doob, Joseph L. (1938). Stochastic processes with an integral-valued parameter. Trans. Amer. Math. Soc. 44: 87–150
- Doob, Joseph L. (1940). Regularity properties of certain families of chance variables. Trans. Amer. Math. Soc. 47: 455–486
- Doob, Joseph L. (1953). Stochastic Processes. Wiley, New York
- Furstenberg, Harry (1963). Non-commuting random products. Trans. Amer. Math. Soc. 108: 377–428
- Furstenberg, Harry, and Harry Kesten (1960). Products of random matrices. Ann. Math. Statist. 31: 457–469
- Gilat, David (1977). Every nonnegative submartingale is the absolute value of a martingale. Ann. Probability 5: 475–481
- Hall, Peter, and C. C. Heyde (1980). Martingale Limit Theory and Its Application. Academic Press, New York
- Halmos, Paul R. (1941). The decomposition of measures. Duke Math. J. 8: 386–392
- Halmos, Paul R.(1950). Measure Theory. Van Nostrand, Princeton
- Hammersley, J. M., and D. J. A. Welsh (1965). First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory. Bernoulli-Bayes-Laplace Anniversary Volume, ed. J. Neyman and L. M. Le Cam, pp. 61–110. Springer, New York
- Hölder, Otto (1889). Ueber einen Mittelwerthssatz. Gesellschaft der Wissenschaften, Göttingen, Nachrichten (= Göttinger Nachrichten), pp. 38–47
- Jensen, J. L. W. V. (1906). Sur les fonctions convexes et les inégalites entre les valeurs moyennes. Acta Math. 30: 175–193
- Kingman, John F. C. (1968). The ergodic theory of subadditive stochastic processes. J. Roy. Statist. Soc. (Ser. B) 30: 499–510
- Kingman, John F. C. (1973). Subadditive ergodic theory (With discussion). Ann. Probability 1: 883–899
- Kingman, John F. C.(1976). Subadditive processes. école d'été de probabilités de St-Flour, 1975. Lecture Notes in Math. (Springer) 539: 167–223
- Kolmogoroff, Andrei N. [Kolmogorov, A.N.] (1933). Grundbegriffe der Wahrscheinlich-keitsrechnung. Springer, Berlin. 2d English ed., Foundations of the Theory of Probability, transl. ed. Nathan Morrison. Chelsea, New York, 1956
- Lamb, Charles W. (1973). A short proof of the martingale convergence theorem. Proc. Amer. Math. Soc. 38: 215–217
- Ledrappier, F. (1984). Quelques propriétés des exposants caractéristiques. école d'été de probabilités de St-Flour, 1982. Lecture Notes in Math. (Springer) 1097: 305–396
- Levental, Shlomo (1988). A proof of Liggett's version of the subadditive ergodic theorem. Proc. Amer. Math. Soc. 102: 169–173
- Lévy, Paul (1937). Théorie de l'addition des variables aléatoires. 2d. ed. 1954. Gauthier-Villars, Paris
- Liggett, Thomas M. (1985). An improved subadditive ergodic theorem. Ann. Probability 13: 1279–1285
- Meyer, Paul-André (1972). Martingales and Stochastic Integrals I. Lecture Notes in Math. 284 (Springer): Berlin
- Neveu, J. (1983). Courte démonstration du théorème ergodique sur-additif. Ann. Inst. Henri Poincaré (Ser. B) 19: 87–90
- Random House Dictionary of the English Language (1987), 2d ed., unabridged, Random House, New York
- Riesz, F. (1945). Sur la théorie ergodique. Comment. Math. Helvetici 17: 221–239
- *Ville, Jean (1939). étude critique de la notion de collectif. Gauthier-Villars, Paris
- *Vitali, Giuseppe (1904–05). Sulle funzioni integrali. Atti Accad. Sci. Torino 40: 1021–1034
- *Vitali, Giuseppe(1907). Sull'integrazione per serie. Rend. Circolo Mat. Palermo 23: 137–155
Reference Title: References
Reference Type: reference-list
- de Acosta, Alejandro (1982). Invariance principles in probability for triangular arrays of B-valued random vectors and some applications. Ann. Probability 10: 346–373
- Aganbegyan, A. G., A. D. Aleksandrov, D. K. Faddeev, M. K. Gavurin, S. S. Kuteladze, V. L. Makarov, Yu. G. Reshetnyak, I. V. Romanovskii, G. Sh. Rubinshtein, and S. L. Sobolev (1987). Leonid Vital'evich Kantorovich. Russian Math. Surveys 42, no. 2: 225–232. Transl. from Uspekhi Mat. Nauk 42, no. 2: 177–182
- Akilov, G. P., B. Z. Vulikh, M. K. Gavurin, V. A. Zalgaller, I. P. Natanson, A. G. Pinsker, and D. K. Faddeev (1962). Leonid Vital'evich Kantorovich (In honor of his fiftieth birthday). Russian Math. Surveys 17, no. 4: 115–128. Transl. from Uspekhi Mat. Nauk 17, no. 4: 201–215
- Alexandroff, Alexander Danilovich [Aleksandrov, A. D.] (1940, 1941, 1943). Additive set-functions in abstract spaces. Mat. Sbornik (N.S.) 8: 307–348; 9: 563–628; 13: 169–238 (in English)
- Alexandroff [Aleksandrov], P. S., N. V. Efimov, V. A. Zalgaller, and A. V. Pogorelov (1973). Aleksandr Danilovich Aleksandrov (on his sixtieth birthday). Russian Math. Surveys 28, no. 2: 225–230. Transl. from Uspekhi Mat. Nauk 28, no. 2: 249–253
- Bray, H. E. (1918–1919). Elementary properties of the Stieltjes integral. Ann. Math. (Ser. 2) 20: 177–186
- *Cantelli, Francesco Paolo (1933). Sulla determinazione empirica della leggi di probabilità. Giorn. Ist. Ital. Attuari, 4: 421–424
- Dall'Aglio, Giorgio (1956). Sugli estremi dei momenti delle funzioni di ripartizione doppia. Ann. Scuola Norm. Sup. Pisa (Ser. 3) 10: 35–74
- Dudley, R. M. (1966). Convergence of Baire measures. Studia Math. 27: 251–268
- Dudley, R. M. (1968). Distances of probability measures and random variables. Ann. Math. Statist. 39: 1563–1572
- Dudley, R. M. (1976). Probabilities and Metrics. Lecture Notes Ser. No. 45, Matematisk Institut, Aarhus Universitet
- Dudley, R. M. (1985). An extended Wichura theorem, definitions of Donsker class, and weighted empirical distributions. Probability in Banach Spaces V (Proc. Conf. Medford, 1984). Ed. A. Beck et al. Lecture Notes in Math. (Springer) 1153: 141–178
- Dyson, Freeman J. (1953). Fourier transforms of distribution functions. Canad. J. Math. 5: 554–558
- Fernique, Xavier (1981). Sur le théorème de Kantorovitch-Rubinstein dans les espaces polonais. Séminaire de Probabilités XV. Lecture Notes in Math. (Springer) 850: 6–10
- Fortet, Robert, and Edith Mourier (1953). Convergence de la répartition empirique vers la répartition théorique. Ann. Sci. Ecole Norm. Sup. 70: 266–285
- *Glivenko, Valery Ivanovich (1933). Sulla determinazione empirica della leggi di probabilità. Giorn. Ist. Ital. Attuari 4: 92–99
- Hall, Marshall, Jr. (1958). A survey of combinatorial analysis. In Some Aspects of Analysis and Probability, pp. 35–104. Wiley, New York
- Hall, Philip (1935). On representatives of subsets. J. London Math. Soc. 10: 26–30
- Halmos, Paul (1946). The theory of unbiased estimation. Ann. Math. Statist. 17: 34–43
- Halmos, Paul(1950). Measure Theory. Van Nostrand, Princeton
- Halmos, Paul, and von Neumann, J. (1942). Operator methods in classical mechanics, II. Ann. Math. 43: 332–350
- *Helly, E. (1911–1912). Über lineare Funktionaloperatoren. Sitzungsber. Nat. Kais. Akad. Wiss. (Wien) Math. Nat. Kl. IIa 121: 265–297
- Hildebrandt, T. H. (1966). Linear continuous functionals on the space (BV) with weak topologies. Proc. Amer. Math. Soc. 17: 658–664
- Hoeffding, Wassily (1948). A class of statistics with asymptotically normal distribution. Ann. Math. Statist. 19: 293–325
- *Hölder, Otto Ludwig (1882). Beiträge zur Potentialtheorie. Dissertation, Tübingen
- Ince, Edward Lindsay (1926). Ordinary Differential Equations. Repr. Dover, New York, 1956
- Istoriia otechestvennoi matematiki (in Russian) (1970). Vol. 4, bk. 2. Acad. Sci. USSR and Ukrain. SSR, Kiev
- Jahrbuch über die Fortschritte der Mathematik, 59 (1933)
- Kantorovich, Leonid Vasilevich (1940). A new method of solving some classes of extremal problems. Comptes Rendus (Doklady)Acad. Sci. USSR 28: 211–214
- Kantorovich, Leonid Vasilevich, and G. Sh. Rubinshtein (1958). On a space of completely additive functions. Vestnik Leningrad Univ. 13, no. 7, Ser. Mat. Astron. Phys. 2: 52–59 (in Russian)
- *König, Dénes (1931). Graphs and matrices. (In Hungarian.) Mat-Fiz. Lapok 38: 116–119
- *König, Dénes(1950). Theorie der endlichen und unendlichen Graphen. Chelsea, New York
- Le Cam, Lucien (1957). Convergence in distribution of stochastic processes. Univ. of Calif. Publs. in Statistics 2, no. 11: 207–236 (Univ. of Calif. Press, Berkeley)
- Liouville, Joseph (1837). Second Mémoire: Sur le développement des fonctions ou parties de fonctions en séries dont les divers termes sont assujettis à satisfaire à une même équation différentielle du second ordre contenant un parametre variable. J. de Math. Pures et Appliquées (Ser. 1) 2: 16–35
- Liouville, Joseph(1838). Premier mémoire. Sur la théorie des équations différentielles linéaires et sur le développement des fonctions en séries. J. de Math. Pures et Appliquées (Ser. 1) 3: 561–614
- Lipschitz, Rudolf Otto Sigismund (1876). Sur la possibilité d'intégrer complètement un système donné d'équations différentielles. Bull. Sci. Math. (Ser. 1) 10: 149–159
- von Mises, R. (1947). On the asymptotic distribution of differentiable statistical functionals. Ann. Math. Statist. 18: 309–348
- *Monge, Gaspard (1781). Mémoire sur la théorie des déblais et des remblais. In Histoire de l'Académie des Sciences de Paris, avec les Mémoires de mathématique et de physique pour la mêeme année, pp. 666–704
- New York Times [unsigned] (1986). Leonid V. Kantorovich dies; Won Nobel Economics Prize. April 11, 1986, p. D18
- Parthasarathy, K. R. (1967). Probability Measures on Metric Spaces. Academic Press, New York
- Picard, Émile (1893). Sur l'application des méthodes d'approximation successives a l'étude de certaines équations différentielles ordinaires. J. de Math. Pures et Appliquées (Ser. 4) 9: 217–271
- Preiss, David (1973). Metric spaces in which Prohorov's theorem is not valid. Z. Wahrscheinlichkeitsth. verw. Geb. 27: 109–116
- Prohorov, Yurii Vasilevich (1956). Convergence of random processes and limit theorems in probability theory. Theor. Probability Appls. 1: 157–214
- Rachev, Svetlozar T. (1984). The Monge-Kantorovich mass transference problem and its stochastic applications. Theor. Probability Appls. 29: 647–676
- Ranga Rao, R. (1962). Relations between weak and uniform convergence of measures with applications. Ann. Math. Statist. 33: 659–680
- Rokhlin, Vladimir Abramovich (1949). On the fundamental ideas of measure theory. Mat. Sbornik 25: 107–150. (In Russian); Amer. Math. Soc. Translations 71 (1952): 1–54
- Rubinshtein, Gennadii Shlemovich (1970). Duality in mathematical programming and certain problems in convex analysis. Russian Mathematical Surveys 25: no. 5: 171–201
- *Salvemini, T. (1943). Sull calcolo degli indici di concordanza tra due caratteri quantitativi. In Atti della VI Riunione della Soc. Ital. di Statistica. Rome
- Scarf, Herbert E. (1975). The 1975 Nobel Prize in Economics: Resource allocation. Science 190: 649, 710, 712
- Schay, Geza, (1974). Nearest random variables with given distributions. Ann. Probability 2: 163–166
- Sherbert, Donald S. (1964). The structure of ideals and point derivations in Banach algebras of Lipschitz functions. Trans. Amer. Math. Soc. 111: 240–272
- Shortt, Rae Michael (1984). Universally measurable spaces: An invariance theorem and diverse characterizations. Fund. Math. 121: 169–176
- Skorohod, Anatolii Vladimirovich (1956). Limit theorems for stochastic processes. Theor. Probability Appls. 1: 261–290
- Strassen, V. (1965). The existence of probability measures with given marginals. Ann. Math. Statist. 36: 423–439
- *Szpilrajn, E. (1937). On absolutely measurable sets and functions (in Polish). C. R. Soc. Sci. Lett. Varsovie CI. III 30:39–68
- Szulga, Alicja (1978). On the Wasserstein metric. Trans. Eighth Prague Conf. Information Theory, Statistical Decision Functions Random Processes, vol. B, pp. 267–273. Reidel, Dordrecht
- Szulga, Alicja(1982). On minimal metrics in the space of random variables. Theory Probability Appls. 27: 424–430
- Varadarajan, Veeravalli S. (1958). On the convergence of sample probability distributions. Sankhyā, 19: 23–26
- Vershik, A. M. (1970). Some remarks on infinite-dimensional linear programming problems. Russian Mathematical Surveys 25, no. 5: 117–124
- Vulikh, B. Z., M. K. Gavurin, A. N. Kolmogorov, Yu. V. Linnik, V. L. Makarov, B. S. Mityagin, A. G. Pinsker, G. S. Rubinshtein, and D. K. Faddev (1972). Leonid Vitalevich Kantorovich (On his 60th birthday). Russian Math. Surveys 27, no. 3: 193–201. Transl. from Uspekhi Mat. Nauk 27, no. 3: 221–227
- Wichura, M. J. (1970). On the construction of almost uniformly convergent random variables with given weakly convergent image laws. Ann. Math. Statist. 41: 284–291
Reference Title: References
Reference Type: reference-list
- de Acosta, Alejandro (1983). A new proof of the Hartman-Wintner law of the iterated logarithm. Ann. Probability 11: 270–276
- Andersen, Erik Sparre, and Börge Jessen (1948). On the introduction of measures in infinite product sets. Danske Vid. Selsk. mat.-Fys. Medd. 25, no. 4. 8 pp.
- André, Désiré (1887). Solution directe du problème résolu par M. Bertrand. Comptes Rendus Acad. Sci. Paris 105: 436–437
- *Bachelier, Louis Jean Baptiste Alphonse (1900). Théorie de la spéculation. Ann. Ecole Norm. Sup. (Ser. 3) 17: 21–86
- *Bachelier, Louis Jean Baptiste Alphonse (1910). Mouvement d'un point ou d'un système matérial soumis à l'action de forces dépendant du hasard. Comptes Rendus Acad. Sci. Paris 151: 852–855
- *Bachelier Louis Jean Baptiste Alphonse (1939). Les nouvelles méthodes du calcul des probabilités. Gauthier–Villars, Paris
- Bingham, N H. (1986). Variants on the law of the iterated logarithm. Bull. London Math. Soc. 18: 433–467
- Bochner, Salomon (1955). Harmonic Analysis and the Theory of Probability. University of Calif. Press, Berkeley and Los Angeles
- Breiman, Leo (1968). Probability. Addison-Wesley, Reading, Mass
- Browder, Felix, E H. Spanier, and M. Gerstenhaber (eds.) (1966). Norbert Wiener, 1894–1964. Amer. Math. Soc., Providence, R. I. Also in Bull Amer. Math. Soc. 72, no. 1, Part II
- Brown, Robert (1828). A Brief Description of Microscopical Observations made in the Months of June, July and August 1827, on the Particles contained in the Pollen of Plants; and on the General Existence of Active Molecules in Organic and Inorganic Bodies. London. German transl. in Ann. Phys. 14 (1828): 294–313
- Doob, Joseph L. (1938). Stochastic processes with an integral-valued parameter. Trans. Amer. Math. Soc. 44: 87–150
- Doob, Joseph L. (1949). Heuristic approach to the Kolmogorov-Smirnov theorems. Ann. Math. Statist. 20: 393–403
- Doob, Joseph L. (1953). Stochastic Processes. Wiley, New York
- Doob, Joseph L. (1966). Wiener's work in probability theory. In Browder et al. (1966), pp.69–71
- Dubins, Lester (1968). On a theorem of Skorohod. Ann. Math. Statist. 39: 2094–2097
- Dudley, R M., Jacob Feldman, and Lucien Le Cam (1972). Some remarks concerning priorities, in connection with our paper “On seminorms and probabilities.” Ann. Math. 95: 585
- Einstein, Albert (1905). On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat [in German]. Ann. Phys. (Ser. 4) 17: 549–560. English transl. in Einstein (1926), pp. 1–18
- Einstein, Albert (1906). Zur Theorie der Brownschen Bewegung. Ann. Phys. (Ser. 4) 19: 371–381. Transl. in Einstein (1926)
- Einstein, Albert (1926). Investigations on the theory of the Brownian movement. Ed. with notes by R. Fürth. Transl. by A D. Cowper. E P. Dutton, New York
- Félix, Lucienne (1970). Bachelier, Louis. Dictionary of Scientific Biography, 1, pp. 366–367. Scribner's, New York
- Feller, Willy (1943). The general form of the so-called law of the iterated logarithm. Trans. Amer. Math. Soc. 54: 373–402
- Feller, Willy (1968). An Introduction to Probability Theory and Its Applications, 1, 3d ed. Wiley, New York
- Fourier, Joseph B J. (1822). Théorie analytique de la chaleur. Gauthier-Villars, Paris
- Frolik, Zdenek (1972). Projective limits of measure spaces. Proc. Sixth Berkeley Symp. Math. Statist. Prob. 2: 67–80. Univ. of Calif. Press, Berkeley and Los Angeles
- Grattan-Guinness, I[vor] (1972). Joseph Fourier, 1768–1830: A survey of his life and work based on a critical edition of his monograph on the propagation of heat, presented to the Institut de France in 1807. M. I. T. Press, Cambridge, Mass
- Hardy, Godfrey H. (1934). Raymond Edward Alan Christopher Paley. J. London Math Soc. 9: 76–80
- Hartman, Philip, and Aurel Wintner (1941). On the Law of the iterated logarithm. Amer. J. Math. 63: 169–176
- Herivel, John (1975). Joseph Fourier: The man and the physicist. Clarendon Press, Oxford
- Hunt, Gilbert A. (1956), Some theorems concerning Brownian motion. Trans. Amer. Math. Sco. 81: 294–319
- Itô, Kiyosi (1944). Stochastic integral. Proc. Imp. Acad. Tokyo 20: 519–524
- Itô, Kiyosi, and Henry P. McKean, Jr. (1965). Diffusion Processes and Their Sample Paths. Springer, New York
- Kac, Mark, Jack Kiefer, and Joseph Wolfowitz (1955). On tests of normality and other tests of goodness of fit based on distance methods. Ann. Math. Statist. 26: 189–211
- Kahane, Jean-Pierre (1976). Commentary on Paley et al. (1933). In Wiener (1976), 1, pp. 558–563
- Kakutani, Shizuo (1944). On Brownian motions in n-space. Proce. Imp. Acad. Tokyo 20: 648–652
- Kesten, Harry (1970). The limit points of a normalized random walk. Ann. Math. Statist. 41: 1173–1205
- Khinchin, Alexander Yakovlevich (1923). Über dyadische Brüche. Math. Z. 18: 109–116
- Khinchin, Alexander Yakovlevich (1924). Über einen Satz der Wahrscheinlichkeitsrechnung. Fund. Math. 6: 9–20
- Khinchin, Alexander Yakovlevich (1933). Asymptotische Gesetze der Wahrscheinlichkeitsrechnung. Springer, Berlin; Chelsea, New York (1948)
- Klass, Michael J. (1976, 1977). Toward a universal law of the iterated logarithm. Part I, Z. Wahrscheinlichkeitsth. verw. Geb. 36: 165–178, Part II, ibid. 39: 151–165
- Kolmogorov, Andrei N. (1929). Über das Gesetz des iterierten Logarithmus. Math. Ann. 101: 126–135
- Kolmogorov, Andrei N. (1933a). Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer, Berlin. Transl. as Foundations of Probability. Chelsea, New York (1956)
- Kolmogorov, Andrei N. (1933b). Sulla determinazione empirica di una legge di distribuzione (in Italian). Giorn. Ist. Ital. Attuar. 4: 83–91. Russian transl. in Kolmogorov (1986), 134–141
- Kolmogorov, Andrei N. (1986). Probability Theory and Mathematical Statistics (selected works; in Russian). Moscow, Nauka
- Kostka, D G. (1973). On Khintchine's estimate for large deviations. Ann. Probability 1: 509–512
- Kuiper, Nicolaas H. (1960). Tests concerning random points on a circle. Proc. Kon. Akad. Wetensch. A (Indag. Math. 22) 63: 38–47
- Laplace, Pierre Simon de (1809). Mémoire sur divers points d'analyse. J. Ecole Polytechnique, cahier 15, tome 8, pp. 229–264; Oeuvres, XIV, pp. 178–214, esp. pp. 184–193
- Levinson, Norman (1966). Wiener's life. In Browder et al. (1966), pp. 1–32
- Lévy, Paul (1939). Sur certains processus stochastiques homogènes. Compositio Math. 7: 283–339
- Lévy, Paul (1948). Processus stochastiques et mouvement brownien. Gauthier-Villars, Paris
- Loève, Michel (1977). Probability Theory 1. 4th ed. Springer, New York
- Martikainen, A I. (1980). A converse to the law of the iterated logarithm for a random walk. Theory Probability Appl. 25: 361–362
- McKean, Henry P. (1969). Stochastic Integrals. Academic Press, New York
- Paley, Raymond Edward Alan Christopher, Norbert Wiener, and Antoni Zygmund (1933). Notes on random functions. Math. Z. 37: 647–668. Also in Wiener (1976), 1, pp. 536–557
- Paley, Raymond Edward Alan Christopher, and N. Wiener (1934). Fourier Transforms in the complex domain. Amer. Math. Soc. Colloq. Publs. 19
- Pinsky, Mark (1969). An elementary derivation of Khintchine's estimate for large deviations. Proc. Amer. Math. Soc. 22: 288–290
- J C. Poggendorffs biographisch-literarisches Handwörterbuch 7b Teil 6 (1979). Paley, R E. A C. Akademie-Verlag, Berlin
- Pruitt, William E. (1981). General one-sided laws of the iterated logarithm. Ann. Probab. 9: 1–48
- Root, David H. (1969). The existence of certain stopping times on Brownian motion. Ann. Math. Statist. 40: 715–718
- Rosalsky, Andrew (1980). On the converse to the iterated logarithm law. Sankhyā Ser. A 42: 103–108
- Segal, Irving Ezra (1954). Abstract probability spaces and a theorem of Kolmogoroff. Amer. J. Math. 76: 721–732
- Segal, Irving Ezra (1956). Tensor algebras over Hilbert spaces, I. Trans. Amer. Math. Soc. 81: 106–134
- Sheu, Shey Shiung (1986). Representing a distribution by stopping a Brownian motion: Root's construction. Bull. Austral. Math. Soc. 34: 427–431
- Skorohod, Anatolii Vladimirovich (1961). Studies in the Theory of Random Processes [in Russian]. Univ. of Kiev. Transl. Addison-Wesley, Reading, Mass. (1965)
- Smirnov, Nikolai Vasil'evich (1939). Estimation of the deviation between empirical distribution curves of two independent samples [in Russian]. Bull. Univ. Moscow 2, no. 2, pp. 3–14. Repr. in Smirnov (1970), pp. 117–127, 267
- Smirnov, Nikolai Vasil'evich (1970). Theory of probability and mathematical statistics: Selected works [in Russian]. Nauka, Moscow
- Smoluchowski, Marian (1906). Zur kinetischen Theorie der Brownschen Molekular-bewegung und der Suspensionen. Ann. Phys. (Ser. 4) 21: 756–780
- Stout, William F. (1974). Almost Sure Convergence. Academic Press, New York
- Strassen, Volker (1964). An invariance principle for the law of the iterated logarithm. Z. Wahrsch. verw. Geb. 3: 211–226
- Strassen, Volker (1966). A converse to the law of the iterated logarithm. Z. Wahrsch. verw. Geb. 4: 265–268
- Thompson, D'Arcy (1959). Growth and Form. Cambridge Univ. Press. (1st ed. 1917.)
- Tucker, Howard G. (1967). A Graduate Course in Probability. Academic Press. New York
- Ulam, Stanislaw (1957). Marian Smoluchowski and the theory of probabilities in physics. Amer. J. Phys. 25: 475–481
- Wiener, Norbert (1923). Differential space. J. Math. Phys. M. I. T. 2: 131–174. Also in Wiener (1976), 1, pp. 455–498
- Wiener, Norbert (1953). Ex-Prodigy: My Childhood and Youth. Simon & Schuster, New York. Repr. M. I. T. Press, Cambridge, Mass. (1964)
- Wiener, Norbert (1956). I Am a Mathematician. Doubleday, New York. Repr. M. I. T. Press, Cambridge, Mass. (1964)
- Wiener, Norbert (1976–1986). Norbert Wiener: Collected Works with Commentaries. Ed. Pesi Masani. 4 vols. M. I. T. Press, Cambridge, Mass
Reference Title: References
Reference Type: reference-list
- Alexandroff [Aleksandrov], P. (1916). Sur la puissance des ensembles mesurables B. Comptes Rendus Acad. Sci. Paris 162: 323–325
- Cohn, Donald Lee (1980). Measure Theory. Birkhäuser, Boston
- Dellacherie, Claude (1978). Quelques exemples familiers, en probabilités, d'ensembles analytiques, non boréliens, Séminaire de Probabilités, Univ. Strasbourg (1976–1977); Lecture Notes in Math. (Springer) 649: 746–756
- Hausdorff, Felix (1916). Die Mächtigkeit der Borelschen Mengen. Math. Ann. 77: 430–437
- Kuratowski, Kazimierz [Casimir] (1933). Topologie I. Monografje Matematyczne, Warsaw and Lwow
- Kuratowski, Kazimierz [Casimir] (1934). Sur une généralisation de la notion d'homéomorphie. Fund. Math. 22: 206–220
- Kuratowski, Kazimierz [Casimir] (1966). Topology, vol. 1, transl. from 2d French ed. (1958) by J. Jaworowski. Academic Press, New York; PWN, Warsaw
- Lebesgue, Henri (1905). Sur les fonctions représentables analytiquement. Journal de Mathématiques (Ser. 6) 1: 139–216
- Lusin [Luzin], Nikolai Nikolaevich (1917). Sur la classification de M. Baire. Comptes Rendus Acad. Sci. Paris 164: 91–94
- Lusin [Luzin] Nikolai Nikolaevich (1930). Leçons sur les ensembles analytiques et leurs applications, with a Note by W. Sierpiński and a preface by H. Lebesgue. Gauthier-Villars, Paris
- Mauldin, R. Daniel, and Stanislaw M. Ulam (1987). Mathematical problems and games. Adv. Appl. Math. 8: 281–344
- Paplauscas [Paplauskas], A. B. (1973). Luzin, Nikolai Nikolaievich. Dictionary of Scientific Biography, 8: 557–559
- Parthasarathy, K. R. [Kalyanapuram Rangachari] (1967). Probability Measures on Metric Spaces. Academic Press, New York
- Sierpiński, Wacław (1950). Les ensembles projectifs et analytiques. In Mémorial des Sciences Mathématiques, fasc. 112. Gauthier-Villars, Paris
- Souslin [Suslin], Mikhail Yakovlevich (1917). Sur une définition des ensembles mesurables B sans nombres transfinis. Comptes Rendus Acad. Sci. Paris 164: 88–91
- Souslin [Suslin], Mikhail Yakovlevich (1920). [Problem]. Fund. Math. 1: 223
- Yushkevich, A. P. (1968). Istoriya Matematiki v Rossii do 1917 goda [in Russian]. Nauka, Moscow
Reference Title: Reference
Reference Type: reference-list
- Bishop, Errett (1967). Foundations of Constructive Analysis. McGraw-Hill, New York
- Church, Alonzo (1956). Introduction to Mathematical Logic, I. Princeton University Press
- Cohen, Paul J. (1963–1964). The independence of the continuum hypothesis. Proc. Nat. Acad. Sci. USA 50: 1143–1148, 51: 105–110
- Cohen, Paul J.(1966). Set Theory and the Continuum Hypothesis. Benjamin, New York
- Dedekind, Richard (1888). Was sind und was sollen die Zahlen? Braunschweig
- Fraenkel, Abraham A., Yehoshua Bar-Hillel, and Azriel Levy (1973). Foundations of Set Theory. 2d ed. North-Holland, Amsterdam
- Fundamenta Mathematicae 109 (1980). Obituary of K. Kuratowski. P. ⅰ–ⅱ
- GÖdel, Kurt (1940). The Consistency of the Continuum Hypothesis. Annals of Math. Studies, no. 3. Princeton University Press
- van Heijenoort, Jean (1967). From Frege to GÖdel: A Source Book in Mathematical Logic, 1879–1931. Harvard University Press
- Kelley, John L. (1955). General Topology. Van Nostrand, Princeton
- Kleene, Stephen C. (1952). Introduction to Matamathematics. Van Nostrand, Princeton
- Kleene, Stephen C.(1967). Mathematical Logic. Wiley, New York
- Krivine, Jean-Louis (1971). Introduction to Axiomatic Set Theory. Reidel, Dordrecht
- Kuratowski, Kazimierz (1921). Sur la notion d'ordre dans la théorie des ensembles. Fund. Math. 2: 161–171
- Landau, Edmund (1930). Foundations of Analysis. Transl. Chelsea, New York, 1951
- MacLane, Saunders (1971). Categories for the Working Mathematician. Springer, New York
- Nelson, Edward (1977). Internal set theory: A new approach to nonstandard analysis. Bull. Amer. Math. Soc. 83: 1165–1198
- Peano, Giuseppe (1889). Arithmetices principia, nova methodo exposita. Turin. Also in Opere scelte, II, pp. 20–55. (Edizioni Cremonese, Rome); 2, transl. in van Heijenoort (1967), pp. 85–97
- Peano, Giuseppe(1891). Sul concetto di numero. Rivista di Matematica 1: 87–102, 256–267
- Quine, Willard Van Orman (1951). Mathematical Logic. 2d ed. Harvard University Press
- Robinson, Abraham (1979). Selected Papers of Abraham Robinson. Vol. II, Nonstandard Analysis and Philosophy. Edited and with introductions by W. A. J. Luxemburg and S. KÖrner. Yale University Press
- Sierpiński, Waclaw (1934, 1956). Hypothèese du continu. Monografje Matematyczne, War-saw. 2d ed., “Containing as Appendix a number of research papers, 1934–1956.” Chelsea, New York
- Sierpiński, Waclaw(1947). L'hypothèese généralisée du continu et l'axiome du choix. Fundamenta Mathematicae 34: 1–5. Repr. in Sierpiński (1957)
- Struik, Dirk J. (1948). A Concise History of Mathematics. 2d ed. Dover, New York
- Suppes, Patrick (1960). Axiomatic Set Theory. Van Nostrand, Princeton
- Wiener, Norbert (1914). A simplification of the logic of relations. Proc. Camb. Philos. Soc. 17: 387–390
Reference Title: References
Reference Type: reference-list
- Ahlfors, Lars Valerian (1979). Complex Analysis. 3d ed. McGraw-Hill, New York
- Courant, R. (1937). Differential and Integral Calculus, Vol. I, 2d ed., transl. by E. J. McShane. Interscience, New York
- Marsden, Jerrold E. (1973). Basic Complex Analysis. W. H. Freeman, San Francisco
- Rudin, Walter (1976). Principles of Mathematical Analysis. 3d ed. McGraw-Hill, New York
Reference Title: References
Reference Type: reference-list
- Banach, Stefan, and Casimir [Kazimierz] Kuratowski (1929). Sur une généralisation du problèeme de la mesure. Fund. Math. 14: 127–131
- Jech, Thomas (1978). Set Theory. Academic Press, New York
Reference Title: Reference
Reference Type: reference-list
- Stromberg, Karl R. (1981). An Introduction to Classical Real Analysis. Wadsworth, Belmont, Calif
Reference Title: References
Reference Type: reference-list
- Bledsoe, Woodrow W., and Anthony P. Morse (1955). Product measures. Trans. Amer. Math. Soc. 79: 173–215
- Blumenthal, R. M. and R. K. Getoor (1968). Markov Processes and Potential Theory. Academic Press, New York
- Bourbaki, N. (1952–1969). Intégration, Chaps. 1–4, (1952), 2d ed. (1965); Chap. 5, (1956), 2d ed. (1965); Chap. 6 (1959); Chaps. 7–8 (1963); Chap. 9 (1969). Hermann, Paris
- Doob, Joseph L. (1947). Probability in functions space. Bull. Amer. Math. Soc. 53: 15–30
- Dudley, R. M. (1972, 1973). A counterexample on measurable processes. Proc. 6th Berkeley Symp. Math. Statist. Prob. (Univ. of Calif. Press) 2: 57–66; Correction, Ann. Probability 1: 191–192
- Dudley, R. M.(1990). Nonmetric compact spaces and nonmeasurable processes. Proc. Amer. Math. Soc. 108: 1001–1005
- Halmos, Paul, R. (1950). Measure Theory. Van Nonstrand, Princeton
- Kakutani, Shizuo (1943). Notes on infinite product spaces, II. Proc. Imp. Acad. Tokyo 19: 184–188
- Nelson, Edward (1959). Regular probability measures on function space. Ann. Math. 69: 630–643
- Tjur, Tue (1980). Probability Based on Radon Measures. Wiley, New York



