The sources of Kolmogorov's Grundbegriffe

Statistical Science

Volumn 21, Issue 1, 2006, Pages 70-98

  Shafer, Glenn ^a,b   Vovk, Vladimir ^b  

^a RUTGERS BUSINESS SCHOOL   (United States)

^b UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Axioms for probability; Borel; Classical probability; Cournot's principle; Frequentism; Grundbegriffe der Wahrscheinlichkeitsrechnung; History of probability; Kolmogorov; Measure theory

Indexed keywords

EID: 33745916794     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/088342305000000467     Document Type: Review

References (197)

1. ANDERSEN, E. S. and JESSEN, B. (1948). On the introduction of measures in infinite product sets. Det Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddelelser 25 (4), 8 pp.
2. BACHELIER, L. (1900). Théorie de la spéculation. Ann. Sci. École Norm. Supér. (3) 17 21-86. This was Bachelier's doctoral dissertation.
3. Reprinted in facsimile in 1995 by Éditions Jacques Gabay, Paris. An English translation, by A. J. Boness, appears in P. H. Cootner, ed. (1964). The Random Character of Stock Market Prices 17-78. MIT Press.
4. BACHELIER, L. (1910). Les probabilités à plusieurs variables. Ann. Sci. École Norm. Supér. (3) 27 339-360.
5. BACHELIER, L. (1912). Calcul des probabilités. Gauthier-Villars, Paris.
6. BARONE, J. and NOVIKOFF, A. (1978). A history of the axiomatic formulation of probability from Borel to Kolmogorov. I. Arch. Hist. Exact Sci. 18 123-190.
7. BARTLETT, M. S. (1949). Probability in logic, mathematics and science. Dialectica 3 104-113.
8. BAYER, R., ed. (1951). Congrès international de philosophie des sciences, Paris, 1949 4. Calcul des probabilités. Hermann, Paris.
9. BERNOULLI, J. (1713). Ars Conjectandi. Thurnisius, Basel. This pathbreaking work appeared eight years after Bernoulli's death. A facsimile reprinting of the original Latin text is sold by Éditions Jacques Gabay, Paris.
10. A German translation appeared in 1899 (Wahrscheinlichkeitsrechnung von Jakob Bernoulli. Anmerkungen von R. Haussner, Ostwald's Klassiker, Nr. 107-108, Engelmann, Leipzig), with a second edition (Deutsch, Frankfurt) in 1999. A Russian translation of Part IV, which contains Bernoulli's law of large numbers, appeared in 1986: Nauka, Moscow. It includes a preface by Kolmogorov, dated October 1985, and commentaries by other Russian authors. B. Sung's English translation of Part IV, dated 1966, remains unpublished but is available in several university libraries in the United States. O. Sheynin's English translation of Part IV, dated 2005, can be downloaded from www.sheynin.de.
11. BERNSTEIN, F. (1912). Über eine Anwendung der Mengenlehre auf ein aus der Theorie der säkularen Störungen herrührendes Problem. Math. Am. 71 417-439.
12. BERNSTEIN, S. N. (1917). (On the axiomatic foundation of the theory of probality). (Communications of the Kharkiv Mathematical Society) 15 209-274. Reprinted in S. N. Bernstein (1964). 10-60. Nauka, Moscow.
13. BERNSTEIN, S. N. (1927). (Theory of Probability). (State Publishing House), Moscow and Leningrad. Second edition 1934, fourth 1946. This work was included in the Grundbegriffe's bibliography.
14. BERTRAND, J. (1889). Calcul des probabilités. Gauthier-Villars, Paris. Some copies of the first edition are dated 1888. Second edition 1907. Reprinted by Chelsea, New York, 1972.
15. BLACKWELL, D. (1956). On a class of probability spaces. Proc. Third Berkeley Symp. Math. Statist. Probab. 2 1-6. Univ. California Press, Berkeley.
16. BLUM, A. and MESPOULET, M. (2003). L'Anarchie bureaucratique. Statistique et pouvoir sous Staline. Découverte, Paris.
17. BOHLMANN, G. (1901). Lebensversicherungs-Mathematik. In Encyklopädie der Mathematischen Wissenschaften 1(2) 852-917. Teubner, Leipzig.
18. BOREL, E. (1895). Sur quelques points de la théorie des fonctions. Ann. Sci. École Norm. Supér. (3) 12 9-55.
19. BOREL, E. (1897). Sur les séries de Taylor. Acta Math. 20 243-247. Reprinted in Borel (1972) 2 661-665.
20. BOREL, E. (1898). Leçons sur la théorie des fonctions. Gauthier-Villars, Paris.
21. BOREL, E. (1905). Remarques sur certaines questions de probabilité. Bull. Soc. Math. France 33 123-128. Reprinted in Borel (1972) 2 985-990.
22. BOREL, E. (1906). La valeur pratique du calcul des probabilités. La revue du mois 1 424-437. Reprinted in Borel (1972) 2 991-1004.
23. BOREL, E. (1909a). Les probabilités dénombrables et leurs applications arithmétiques. Rend. Circ. Mat. Palermo 27 247-270. Reprinted in Borel (1972) 2 1055-1079.
24. BOREL, E. (1909b). Éléments de la théorie des probabilités. Gauthier-Villars, Paris. Third edition 1924.
25. The 1950 edition was translated into English by J. E. Freund and published as Elements of the Theory of Probability by Prentice-Hall in 1965.
26. BOREL, E. (1912). Notice sur les travaux scientifiques. Gauthier-Villars, Paris. Prepared by Borel to support his candidacy to the Académie des Sciences. Reprinted in Borel (1972) 1 119-190.
27. BOREL, E. (1914). Le Hasard. Alcan, Paris. The first and second editions both appeared in 1914, with later editions in 1920, 1928, 1932, 1938 and 1948.
28. BOREL, E. (1930). Sur les probabilités universellement négligeables. C. R. Acad. Sci. Paris 190 537-540. Reprinted as Note IV of Borel (1939).
29. BOREL, E. (1939). Valeur pratique et philosophie des probabilités. Gauthier-Villars, Paris. Reprinted in 1991 by Éditions Jacques Gabay, Paris.
30. BOREL, E. (1972). Uvres de Émile Borel. Centre National de la Recherche Scientifique, Paris. Four volumes.
31. BOURBAKI, N. (pseudonym) (1994). Elements of the History of Mathematics. Springer, Berlin. Translated from the 1984 French edition by J. Meldrum.
32. BROGGI, U. (1907). Die Axiome der Wahrscheinlichkeitsrechnung. Ph.D. thesis, Universität Göttingen. Excerpts reprinted in Schneider (1988) 359-366.
33. BRU, B. (2001). Émile Borel. In Statisticians of the Centuries (C. C. Heyde and E. Seneta, eds.) 287-291. Springer, New York.
34. BRU, B. (2003). Souvenirs de Bologne. Journal de la Société Française de Statistique 144 134-226. Special volume on history.
35. BRUNS, H. (1906). Wahrscheinlichkeitsrechnung und Kollektivmasslehre. Teubner, Leipzig and Berlin. Available at historical.library.cornell.edu.
36. BUFFON, G.-L. (1777). Essai d'arithmétique morale. In Supplément à l'Histoire naturelle 4 46-148. Imprimerie Royale, Paris.
37. CANTELLI, F. P. (1916a). La tendenza ad un limite nel senso del calcolo delle probabilità. Rend. Circ. Mat. Palermo 41 191-201. Reprinted in Cantelli (1958) 175-188.
38. CANTELLI, F. P. (1916b). Sulla legge dei grandi numeri. Atti Reale Accademia Nationale Lincei, Memorie Cl. Sc. Fis. 11 329-349. Reprinted in Cantelli (1958) 189-213.
39. CANTELLI, F. P. (1917). Sulla probabilità come limite della frequenza. Atti Reale Accademia Nationale Lincei 26 39-45. Reprinted in Cantelli (1958) 214-221.
40. CANTELLI, F. P. (1932). Una teoria astratta del calcolo delle probabilità. Giornale dell'Istituto Italiano degli Attuari 3 257-265. Reprinted in Cantelli (1958) 289-297.
41. CANTELLI, F. P. (1935). Considérations sur la convergence dans le calcul des probabilités. Ann. Inst. H. Poincaré 5 3-50. Reprinted in Cantelli (1958) 322-372.
42. CANTELLI, F. P. (1958). Alcune memorie matematiche. Giuffrè, Milan.
43. CARATHÉODORY, C. (1914). Über das lineare Mass von Punktmengen - eine Verallgemeinerung des Längenbegriffs. Nachr. Akad. Wiss. Göttingen Math.-Phys. II Kl. 4 404-426.
44. CARATHÉODORY, C. (1918). Vorlesungen über reelle Funktionen. Teubner, Leipzig and Berlin. Second edition 1927.
45. CASTELNUOVO, G. (1919). Calcolo delle probabilitá. Albrighi e Segati, Milan, Rome, and Naples. Second edition in two volumes, 1926 and 1928. Third edition 1948.
46. CHUPROV, A. A. (1910). Oyuepku no meopuu cmamucmuku (Essays on the Theory of Statistics), 2nd ed. Sabashnikov, St. Petersburg. The first edition appeared in 1909. The second edition was reprinted by the State Publishing House, Moscow, in 1959.
47. CHURCH, A. (1940). On the concept of a random sequence. Bull. Amer. Math. Soc. 46 130-135.
48. CIFARELLI, D. M. and REGAZZINI, E. (1996). de Finetti's contribution to probability and statistics. Statist. Sci. 11 253-282.
49. COPELAND, A. H., SR. (1932). The theory of probability from the point of view of admissible numbers. Ann. Math. Statist. 3 143-156.
50. COURNOT, A.-A. (1843). Exposition de la théorie des chances et des probabilités. Hachette, Paris. Reprinted in 1984 as Volume I (B. Bru, ed.) of Cournot (1973-1984).
51. COURNOT, A.-A. (1973-1984). Œuvres complètes. Vrin, Paris. Ten volumes, with an eleventh to appear.
52. CZUBER, E. (1903). Wahrscheinlichkeitsrechnung und ihre Anwendung auf Fehlerausgleichung, Statistik und Lebensversicherung. Teubner, Leipzig. Second edition 1910, third 1914.
53. D'ALEMBERT, J. (1761). Réflexions sur le calcul des probabilités. Opuscules mathématiques 21-25.
54. D'ALEMBERT, J. (1767). Doutes et questions sur le calcul des probabilités. Mélanges de littérature, d'histoire, et de philosophie 5 275-304.
55. DANIELL, P. J. (1918). A general form of integral. Ann. of Math. (2) 19 279-294.
56. DANIELL, P. J. (1919a). Integrals in an infinite number of dimensions. Ann. of Math. (2) 20 281-288.
57. DANIELL, P. J. (1919b). Functions of limited variation in an infinite number of dimensions. Ann. of Math. (2) 21 30-38.
58. DANIELL, P. J. (1920). Further properties of the general integral. Ann. of Math. (2) 21 203-220.
59. DANIELL, P. J. (1921). Integral products and probability. Amer. J. Math. (2) 43 143-162.
60. DASTON, L. (1979). d'Alembert's critique of probability theory. Historia Math. 6 259-279.
61. DASTON, L. (1994). How probabilities came to be objective and subjective. Historia Math. 21 330-344.
62. DE FINETTI, B. (1930). A proposito dell'estensione del teorema delle probabilità totali alle classi numerabili. Rend. Reale Instituto Lombardo Sci. Lettere 63 901-905, 1063-1069.
63. DE FINETTI, B. (1939). Compte rendu critique du colloque de Genève sur la théorie des probabilités. Actualités Scientifiques et Industrielles 766. Hermann, Paris. Number 766 is the eighth fascicle of Wavre (1938-1939).
64. DE MOIVRE, A. (1718). The Doctrine of Chances: Or, A Method of Calculating the Probability of Events in Play. Pearson, London. Second edition 1738, third 1756.
65. DIEUDONNÉ, J. (1948). Sur le théorème de Lebesgue-Nikodym. III. Ann. Univ. Grenoble 23 25-53.
66. DOOB, J. L. (1953). Stochastic Processes. Wiley, New York.
67. DOOB, J. L. (1989). Kolmogorov's early work on convergence theory and foundations. Ann. Probab. 17 815-821.
68. DOOB, J. L. (1994). The development of rigor in mathematical probability, 1900-1950. In Pier (1994b) 157-170. Reprinted in Amer. Math. Monthly 103 (1996) 586-595.
69. DÖRGE, K. (1930). Zu der von R. von Mises gegebenen Begründung der Wahrscheinlichkeitsrechnung. Math. Z. 32 232-258.
70. ELLIS, R. L. (1849). On the foundations of the theory of probabilities. Trans. Cambridge Philos. Soc. 8 1-6. The paper was read on February 14, 1842. Part 1 of Volume 8 was published in 1843 or 1844, but Volume 8 was not completed until 1849.
71. FABER, G. (1910). Über stetige Funktionen. II. Math. Ann. 69 372-443.
72. FECHNER, G. T. (1897). Kollektivmasslehre. Engelmann, Leipzig. Edited by G. F. Lipps.
73. FRÉCHET, M. (1915a). Définition de l'intégrale sur un ensemble abstrait. C. R. Acad. Sci. Paris 160 839-840.
74. FRÉCHET, M. (1915b). Sur l'intégrale d'une fonctionnelle étendue à un ensemble abstrait. Bull. Soc. Math. France 43 248-265.
75. FRÉCHET, M. (1930). Sur l'extension du théorème des probabilités totales au cas d'une suite infinie d'évé nements. Rend. Reale Instituto Lombardo Sci. Lettere 63 899-900, 1059-1062.
76. FRÉCHET, M. (1937-1938). Recherches théoriques modernes sur la théorie des probabilités. Gauthier-Villars, Paris. This work was listed in the Grundbegriffe's bibliography as in preparation. It consists of two books, Fréchet (1937) and Fréchet (1938a). The two books together constitute Fascicle 3 of Volume 1 of Émile Borel's Traité du calcul des probabilités et ses applications.
77. FRÉCHET, M. (1937). Généralités sur les probabilités. Variables aléatoires. Gauthier-Villars, Paris. Second edition 1950. This is Book 1 of Fréchet (1937-1938).
78. FRÉCHET, M. (1938a). Méthode des fonctions arbitraires. Théorie des événements en chaîne dans le cas d'un nombre fini d'états possibles. Gauthier-Villars, Paris. Second edition 1952. This is Book 2 of Fréchet (1937-1938).
79. FRÉCHET, M. (1938b). Exposé et discussion de quelques recherches récentes sur les fondements du calcul des probabilités. Actualités Scientifiques et Industrielles 735 23-55. Hermann, Paris. In Wavre (1938-1939), second fascicle, entitled Les fondements du calcul des probabilités.
80. FRÉCHET, M. (1951). Rapport général sur les travaux du Colloque de Calcul des Probabilités. In Bayer (1951) 3-21.
81. FRÉCHET, M. and HALBWACHS, M. (1924). Le calcul des probabilités à la portée de tous. Dunod, Paris.
82. GNEDENKO, B. V. and KOLMOGOROV, A. N. (1948). (Probability theory). In (Thirty Years of Soviet Mathematics 1917-1947) 701-727. Moscow and Leningrad. English translation in Sheynin (1998) 131-158.
83. GNEDENKO, B. V. and KOLMOGOROV, A. N. (1949). State Publishing House, Moscow. Translated into English by K. L. Chung and published in 1954 as Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, MA, with an appendix by J. L. Doob.
84. HABERMAN, S. J. (1996). Advanced Statistics 1. Description of Populations. Springer, New York.
85. HADAMARD, J. (1922). Les principes du calcul des probabilités. Revue de métaphysique et de morale 39 289-293.
86. A slightly longer version of this note, with the title "Les axiomes du calcul des probabilités," was included in Oeuvres de Jacques Hadamard 4 2161-2162. Centre National de la Recherche Scientifique, Paris, 1968.
87. HAUSDORFF, F. (1901). Beiträge zur Wahrscheinlichkeitsrechnung. Sitzungsber. Königlich Sächs. Gesellschaft Wiss. Leipz. Math.-Phys. Kl. 53 152-178.
88. HAUSDORFF, F. (1914). Grundzüge der Mengenlehre, von Veit, Leipzig.
89. HAWKINS, T. (1975). Lebesgue's Theory of Integration: Its Origins and Development, 2nd ed. Chelsea, New York. First edition 1970, Univ. Wisconsin Press, Madison. The second edition differs only slightly from the first, but it corrects a consequential error on p. 104. Second edition reprinted in 1979 by Chelsea, New York, and then in 2001 by the American Mathematical Society, Providence, RI.
90. HELM, G. (1902). Die Wahrscheinlichkeitslehre als Theorie der Kollektivbegriffe. Annalen der Naturphilosophie 1 364-384.
91. HILBERT, D. (1902). Mathematical problems. Bull. Amer. Math. Soc. 8 437-479. Hilbert's famous address to the International Congress of Mathematicians in Paris in 1900, in which he listed twenty-three open problems central to mathematics. Translated from the German by M. W. Newson.
92. HOCHKIRCHEN, T. (1999). Die Axiomatisierung der Wahrscheinlichkeitsrechnung und ihre Kontexte: Von Hilberts sechstem Problem zu Kolmogoroffs Grundbegriffen. Vandenhoeck and Ruprecht, Göttingen.
93. HOLGATE, P. (1997). Independent functions: Probability and analysis in Poland between the wars. Biometrika 84 161-173.
94. JEFFREYS, H. (1931). Scientific Inference. Cambridge Univ. Press. Second edition 1957, third 1973.
95. JESSEN, B. (1930). Über eine Lebesguesche Integrationstheorie für Funktionen unendlich vieler Veränderlichen. In Den Syvende Skandinaviske Mathatikerkongress I Oslo 19-22 August 1929 127-138. A. W. Brøggers Boktrykkeri, Oslo.
96. JESSEN, B. (1935). Some analytical problems relating to probability. J. Math. Phys. Mass. Inst. Tech. 14 24-27.
97. JOHNSON, N. L. and KOTZ, S., eds. (1997). Leading Personalities in Statistical Sciences. Wiley, New York.
98. KAHANE, J.-P. (1994). Des séries de Taylor au mouvement brownien, avec un aperçu sur le retour. In Pier (1994b) 415-429.
99. KAMLAH, A. (1983). Probability as a quasi-theoretical concept - J. V. Kries' sophisticated account after a century. Erkenntnis 19 239-251.
100. KEYNES, J. M. (1921). A Treatise on Probability. Macmillan, London.
101. KHINCHIN, A. YA. (1929). (Mises' work on probability and the principles of statistical physics). 9 141-166.
102. KHINCHIN, A. YA. (1961). On the Mises frequentist theory. (Questions of Philosophy) 15 (1, 2) 91-102, 77-89. Published after Khinchin's death by B. Gnedenko.
103. English translation in Sheynin (1998) 99-137, reproduced with footnotes by R. Siegmund-Schultze in Science in Context 17 (2004) 391-422. We have seen only this English translation, not the original.
104. KHINCHIN, A. YA. and KOLMOGOROV, A. N. (1925). Über Konvergenz von Reihen, deren Glieder durch den Zufall bestimmt werden. (Sbornik: Mathematics) 32 668-677. Translated into Russian in Kolmogorov (1986) 7-16 and thence into English in Kolmogorov (1992) 1-10.
105. KNOBLOCH, E. (2001). Emile Borel's view of probability theory. In Probability Theory: Philosophy, Recent History and Relations to Science (V. F. Hendricks, S. A. Pedersen and K. F. Jørgensen, eds.) 71-95. Kluwer, Dordrecht.
106. KOLMOGOROV, A. N. (1928). Über die Summen durch den Zufall bestimmter unabhängiger Grössen. Math. Ann. 99 309-319. An addendum appears in 1930: 102 484-488. The article and the addendum are translated into Russian in Kolmogorov (1986) 20-34 and thence into English in Kolmogorov (1992) 15-31.
107. KOLMOGOROV, A. N. (1929). (The General Theory of Measure and the calculus of probability). In (Collected Works of the Mathematical Section, Communist Academy, Section for Natural and Exact Sciences) 1 8-21. The Socialist Academy was founded in Moscow in 1918 and was renamed The Communist Academy in 1923 (Vucinich, 2000). The date 8 January 1927, which appears at the end of the article in the journal, was omitted when the article was reproduced in the second volume of Kolmogorov's collected works (Kolmogorov, 1986, 48-58). The English translation (Kolmogorov, 1992, 48-59) modernizes the article's terminology somewhat: M becomes a "measure" instead of a "measure specification."
108. KOLMOGOROV, A. N. (1931). Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung. Math. Ann. 104 415-458. Dated July 26, 1930. Translated into Russian in Kolmogorov (1986) 60-105 and thence into English in Kolmogorov (1992) 62-108.
109. KOLMOGOROV, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer, Berlin. A Russian translation by G. M. Bavli, appeared under the title (Nauka, Moscow) in 1936, with a second edition, slightly expanded by Kolmogorov with the assistance of A. N. Shiryaev, in 1974, and a third edition (Moscow) in 1998.
110. An English translation by N. Morrison appeared under the title Foundations of the Theory of Probability (Chelsea, New York) in 1950, with a second edition in 1956.
111. KOLMOGOROV, A. N. (1935). (On some modern currents in the theory of probability). In (Proceedings of the 2nd All-Union Mathematical Congress, Leningrad, 24-30 June 1934) 1 (Plenary Sessions and Review Talks) 349-358. AH CCCP, Leningrad and Moscow. English translation in Sheynin (2000) 165-173.
112. KOLMOGOROV, A. N. (1939). Letter to Maurice Fréchet. Fonds Fréchet, Archives de l'Académie des Sciences, Paris.
113. KOLMOGOROV, A. N. (1948). (Obituary for Evgeny Evgenievich Slutsky). (Russian Mathematical Surveys) 3(4) 142-151.
114. English translation in Sheynin (1998) 77-88, reprinted in Math. Sci. 27 67-74 (2002).
115. KOLMOGOROV, A. N. (1956). (Probability theory). In (A. D. Aleksandrov, A. N. Kolmogorov and M. A. Lavrent'ev, eds.) 2 252-284. Nauka, Moscow. The Russian edition had three volumes.
116. The English translation, Mathematics, Its Content, Methods, and Meaning, was first published in 1962 and 1963 in six volumes by the American Mathematical Society, Providence, RI, and then republished in 1965 in three volumes by the MIT Press, Cambridge, MA. Reprinted by Dover, New York, 1999. Kolmogorov's chapter occupies pp. 33-71 of Part 4 in the 1963 English edition and pp. 229-264 of Volume 2 in the 1965 English edition.
117. KOLMOGOROV, A. N. (1992). Selected Works of A. N. Kolmogorov 2. Probability Theory and Mathematical Statistics. Kluwer, Dordrecht. Translation by G. Lindquist of Kolmogorov (1986).
118. LAEMMEL, R. (1904). Untersuchungen über die Ermittlung von Wahrscheinlichkeiten. Ph.D. thesis, Universität Zürich. Excerpts reprinted in Schneider (1988) 367-377.
119. LEBESGUE, H. (1901). Sur une généralisation de l'intégrale définie. C. R. Acad. Sci. Paris 132 1025-1028.
120. LEBESGUE, H. (1904). Leçons sur l'intégration et la recherche des fonctions primitives. Gauthier-Villars, Paris. Second edition 1928.
121. LÉVY, P. (1925). Calcul des probabilités. Gauthier-Villars, Paris.
122. LÉVY, P. (1937). Théorie de l'addition des variables aléatoires. Gauthier-Villars, Paris. Second edition 1954.
123. LÉVY, P. (1959). Un paradoxe de la théorie des ensembles aléatoires. C. R. Acad. Sci. Paris 248 181-184. Reprinted in Levy (1973-1980) 667-69.
124. LÉVY, P. (1973-1980). Œuvres de Paul Lévy. Gauthier-Villars, Paris. In six volumes. Edited by D. Dugué.
125. ŁOMNICKI, A. (1923). Nouveaux fondements du calcul des probabilités (Définition de la probabilité fondée sur la théorie des ensembles). Fund. Math. 4 34-71.
126. ŁOMNICKI, Z. and ULAM, S. (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.
127. LORENTZ, G. G. (2002). Mathematics and politics in the Soviet Union from 1928 to 1953. J. Approx. Theory 116 169-223.
128. LOVELAND, J. (2001). Buffon, the certainty of sunrise, and the probabilistic reductio ad absurdum. Arch. Hist. Exact Sci. 55 465-477.
129. MAC LANE, S. (1995). Mathematics at Göttingen under the Nazis. Notices Amer. Math. Soc. 42 1134-1138.
130. MAISTROV, L. E. (1974). Probability Theory: A Historical Sketch. Academic Press, New York. Translated and edited by S. Kotz.
131. MARKOV, A. A. (1900). (Calculus of Probability). St. Petersburg. Second edition 1908, fourth 1924.
132. MARKOV, A. A. (1912). Wahrscheinlichkeitsrechnung. Teubner, Leipzig. Translation of second edition of Markov (1900). Available at historical.library.cornell.edu.
133. MARTIN, T. (1996). Probabilités et critique philosophique selon Cournot. Vrin, Paris.
134. MARTIN, T. (1998). Bibliographie cournotienne. Annales littéraires de l'Université de Franche-Comté, Besançon.
135. MARTIN, T. (2003). Probabilité et certitude. In Probabilités subjectives et rationalité de T action (T. Martin, ed.) 119-134. CNRS Éditions, Paris.
136. MASANI, P. R. (1990). Norbert Wiener, 1894-1964. Birkhäuser, Basel.
137. MAZLIAK, L. (2003). Andrei Nikolaevitch Kolmogorov (1903-1987). Un aperçu de l'homme et de l'œuvre probabiliste. Prépublication PMA-785, Univ. Paris VI. Available at www.proba.jussieu.fr.
138. MEINONG, A. (1915). Über Möglichkeit und Wahrscheinlichkeit: Beiträge zur Gegenstandstheorie und Erkenntnistheorie. Barth, Leipzig.
139. NIKODYM, O. (1930). Sur une généralisation des intégrales de M. J. Radon. Fund. Math. 15 131-179.
140. ONDAR, KH. O., ed. (1981). The Correspondence Between A. A. Markov and A. A. Chuprov on the Theory of Probability and Mathematical Statistics. Springer, New York. Translated from the Russian by C. M. and M. D. Stein.
141. ONICESCU, O. (1967). Le livre de G. Castelnuovo Calcolo della probabilità e applicazioni comme aboutissant de la suite des grands livres sur les probabilités. In Simposio Internazionale di Geometria Algebrica (Roma, 30 Settembre-5 Ottobre 1965) xxxvii-liii. Edizioni Cremonese, Rome.
142. PIER, J.-P. (1994a). Intégration et mesure 1900-1950. In Pier (1994b) 517-564.
143. PIER, J.-P., ed. (1994b). Development of Mathematics 1900-1950. Birkhäuser, Basel.
144. POINCARÉ, H. (1890). Sur le problème des trois corps et les équations de la dynamique. Acta Math. 13 1-271.
145. POINCARÉ, H. (1896). Calcul des probabilités. Leçons professées pendant le deuxième semestre 1893-1894. Carré, Paris. Available at historical.library.cornell.edu.
146. POINCARÉ, H. (1912). Calcul des probabilités. Gauthier-Villars, Paris. Second edition of Poincaré (1896).
147. PORTER, T. (1986). The Rise of Statistical Thinking, 1820-1900. Princeton University Press, Princeton, NJ.
148. RADEMACHER, H. (1922). Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen. Math. Ann. 87 112-138.
149. RADON, J. (1913). Theorie und Anwendungen der absolut additiven Mengenfunktionen. Akad. Wiss. Sitzungsber. Kaiserl. Math.-Nat. Kl. 122 1295-1438.
150. Reprinted in his Gesammelte Abhandlungen 1 45-188. Birkhäuser, Basel, 1987.
151. REICHENBACH, H. (1916). Der Begriff der Wahrscheinlichkeit für die mathematische Darstellung der Wirklichkeit. Barth, Leipzig.
152. REICHENBACH, H. (1932). Axiomatik der Wahrscheinlichkeitsrechnung. Math. Z. 34 568-619.
153. ROGERS, L. C. G. and WILLIAMS, D. (2000). Diffusions, Markov Processes, and Martingales. 1. Foundations, reprinted 2nd ed. Cambridge Univ. Press.
154. SCHNEIDER, I., ed. (1988). Die Entwicklung der Wahrscheinlichkeitstheorie von den Anfängen bis 1933: Einführungen und Texte. Wissenschaftliche Buchgesellschaft, Darmstadt.
155. SEGAL, I. E. (1992). Norbert Wiener. November 26, 1894-March 18, 1964. Biographical Memoirs 61 388-436. National Academy of Sciences, Washington.
156. SENETA, E. (1997). Boltzmann, Ludwig Edward. In Johnson and Kotz (1997) 353-354.
157. SENETA, E. (2004). Mathematics, religion and Marxism in the Soviet Union in the 1930s. Historia Math. 31 337-367.
158. SHAFER, G. and VOVK, V. (2001). Probability and Finance: It's Only a Game! Wiley, New York.
159. SHAFER, G. and VOVK, V. (2005). The origins and legacy of Kolmogorov's Grundbegriffe. Working Paper No. 4. Available at www.probabilityandfinance.com.
160. SHEYNIN, O. (1996). Aleksandr A. Chuprov: Life, Work, Correspondence. The Making of Mathematical Statistics. Vandenhoeck and Ruprecht, Göttingen.
161. SHEYNIN, O., ed. (1998). From Markov to Kolmogorov. Russian papers on probability and statistics. Containing essays of S. N. Bernstein, A. A. Chuprov, B. V. Gnedenko, A. Ya. Khinchin, A. N. Kolmogorov, A. M. Liapunov, A. A. Markov and V. V. Paevsky. Hänsel-Hohenhausen, Egelsbach, Germany. Translations from Russian into English by the editor. Deutsche Hochschulschriften No. 2514. In microfiche.
162. SHEYNIN, O., ed. (2000). From Daniel Bernoulli to Urlanis. Still more Russian Papers on Probability and Statistics. Hänsel-Hohenhausen, Egelsbach, Germany. Translations from Russian into English by the editor. Deutsche Hochschulschriften No. 2696. In microfiche.
163. SIEGMUND-SCHULTZE, R. (2004). Mathematicians forced to philosophize: An introduction to Khinchin's paper on von Mises' theory of probability. Sci. Context 17 373-390.
164. SIERPIŃSKI, W. (1918). Sur une définition axiomatique des ensembles mesurables (L). Bull. Internat. Acad. Sci. Cracovie A 173-178.
165. Reprinted in W. Sierpiński (1975). Oeuvres choisies 2 256-260. PWN (Polish Scientific Publishers), Warsaw.
166. SLUTSKY, E. (1922). (On the question of the logical foundation of the theory of probability). (Bulletin of Statistics) 12 13-21
167. SLUTSKY, E. (1925). Über stochastische Asymptoten und Grenzwerte. Metron 5 3-89.
168. STEINHAUS, H. (1923). Les probabilités dénombrables et leur rapport à la théorie de la mesure. Fund. Math. 4 286-310.
169. STEINHAUS, H. (1930a). Über die Wahrscheinlichkeit dafür, daß der Konvergenzkreis einer Potenzreihe ihre natürliche Grenze ist. Math. Z. 31 408-416. Received by the editors 5 August 1929.
170. STEINHAUS, H. (1930b). Sur la probabilité de la convergence de séries. Première communication. Studio Math. 2 21-39. Received by the editors 24 October 1929.
171. STIGLER, S. M. (1973). Simon Newcomb, Percy Daniell, and the history of robust estimation 1885-1920. J. Amer. Statist. Assoc. 68 872-879.
172. TORNIER, E. (1933). Grundlagen der Wahrscheinlichkeitsrechnung. Acta Math. 60 239-380.
173. ULAM, S. (1932). Zum Massbegriffe in Produkträumen. In Verhandlung des Internationalen Mathematiker-Kongress Zürich 2118-119.
174. VENN, J. (1888). The Logic of Chance, 3rd ed. Macmillan, London and New York. First edition 1866, second 1876.
175. VILLE, J. (1939). Étude critique de la notion de collectif. Gauthier-Villars, Paris. This differs from Ville's dissertation, which was defended in March 1939, only in that a 17-page introductory chapter replaces the dissertation's one-page introduction.
176. VON BORTKIEWICZ, L. (1901). Anwendungen der Wahrscheinlichkeitsrechnung auf Statistik. In Encyklopädie der Mathematischen Wissenschaften 1 821-851. Teubner, Leipzig.
177. VON KRIES, J. (1886). Die Principien der Wahrscheinlichkeitsrechnung. Eine logische Untersuchung. Mohr, Freiburg. The second edition, which appeared in 1927, reproduced the first without change and added a new 12-page foreword.
178. VON MISES, R. (1919). Grundlagen der Wahrscheinlichkeitsrechnung. Math. Z. 5 52-99.
179. VON MISES, R. (1928). Wahrscheinlichkeit, Statistik und Wahrheit. Springer, Vienna. Second edition 1936, third 1951. A posthumous fourth edition, edited by his widow Hilda Geiringer, appeared in 1972.
180. English editions, under the title Probability, Statistics and Truth, appeared in 1939 and 1957.
181. VON MISES, R. (1931). Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik. Deuticke, Leipzig and Vienna.
182. VON PLATO, J. (1994). Creating Modern Probability: Its Mathematics, Physics, and Philosophy in Historical Perspective. Cambridge Univ. Press.
183. VUCINICH, A. (2000). Soviet mathematics and dialectics in the Stalin era. Historia Math. 27 54-76.
184. WALD, A. (1938). Die Widerspruchfreiheit des Kollectivbegriffes. In Actualités Scientifiques et Industrielles 735 79-99.Hermann, Paris.
185. Titled Les fondements du calcul des probabilités, Number 735 is the second fascicle of Wavre (1938-1939).
186. WAVRE, R. (1938-1939). Colloque consacré à la théorie des probabilités. Hermann, Paris. This celebrated colloquium, chaired by Maurice Fréchet, was held in October 1937 at the University of Geneva. The proceedings were published by Hermann in eight fascicles in their series Actualités Scientifiques et Industrielles. The first seven fascicles appeared in 1938 as numbers 734 through 740; the eighth, de Finetti's summary of the colloquium, appeared in 1939 as number 766 (de Finetti, 1939).
187. WHITTLE, P. (2000). Probability via Expectation, 4th ed. Springer, New York. The first two editions (Penguin, 1970; Wiley, 1976) were titled Probability. The third edition, also by Springer, appeared in 1992.
188. WIENER, N. (1920). The mean of a functional of arbitrary elements. Ann. of Math. (2) 22 66-72.
189. WIENER, N. (1921a). The average of an analytical functional. Proc. Natl. Acad. Sci. U.S.A. 7 253-260.
190. WIENER, N. (1921b). The average of an analytical functional and the Brownian movement. Proc. Natl. Acad. Sci. U.S.A. 7 294-298.
191. WIENER, N. (1923). Differential-space. J. Math. Phys. Mass. Inst. Tech. 2 131-174.
192. WIENER, N. (1924). The average value of a functional. Proc. London Math. Soc. 22 454-467.
193. WIENER, N. (1956). I am a Mathematician. The Later Life of a Prodigy. Doubleday, Garden City, NY.
194. WIENER, N. (1976-1985). Collected Works with Commentaries. MIT Press, Cambridge, MA. Four volumes. Edited by P. Masani. Volume 1 includes Wiener's early papers on Brownian motion (Wiener, 1920; Wiener, 1921a; Wiener, 1921b; Wiener, 1923; Wiener, 1924), with a commentary by K. Itô.
195. WIMAN, A. (1900). Über eine Wahrscheinlichkeitsaufgabe bei Kettenbruchentwicklungen. Öfversigt af Kongliga Svenska Vetenskaps-Akademiens Förhandlingar. Femtiondesjunde Årgången 57 829-841.
196. WIMAN, A. (1901). Bemerkung über eine von Gyldén aufgeworfene Wahrscheinlichkeitsfrage. Håkan Ohlssons boktrykeri, Lund.