Real Analysis and Probability


Real Analysis and Probability

This classic textbook, now reissued, offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The new edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.


 Reviews:

"A marvelous work which will soon become a standard text in the field for both teaching and reference...a complete and pedagogically perfect presentation of both the necessary preparatory material of real analysis and the proofs througout the text. Some of the topics and proofs are rarely found in other textbooks." Proceedings of the Edinburgh Mathematical Society

'Careful, scholarly, and stimulating. It would be a pleasure to teach a mathematically-oriented graduate-level course from this text.' Short Book Reviews of the ISI

'[It] will serve for a long time as a standard reference.' Zentralblatt fur und ihre Grenzgebiete

'What makes the book special … is the care and scholarship with which the material is treated, and the choice of additional topics … not usually covered in first year graduate courses.' Mathematical Reviews

'The book serves as a clear, rigorous, and complete introduction to modern probability theory using methods of mathematical analysis, and a description of relations between the two fields … it could be very useful for students interested in learning both topics, it can also serve as complementary reading to standard lectures. Teachers preparing their graduate level courses can use the book as an excellent, rigorously written and complete source.' EMS Newsletter

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