ADDISON, J. W., 1958. Separation principles in the hierarchies of classical and effective descriptive set theory. Fundamenta Mathematicae 46 123–135.
ARROW, K. J., D. BLACKWELL, and M. A. GIRSHICK, 1949. Bayes and minimax solutions of sequential decision problems. Econometrica 17 213–243.
BACHELIER, LOUIS, 1900. Théorie de la Spéculation. Paris. (Thesis.)
BACHELIER, LOUIS, 1912. Calcul des Probabilités. Gauthier-Villars, Paris.
BACHELIER, LOUIS, 1914. Le Jeu, la Chance et le Hasard. Flammarion, Paris. (Reprinted in 1929.)
BACHELIER, LOUIS, 1938. La Spéculation et le Calcul des Probabilités. Gauthier-Villars, Paris.
BAHADUR, R. R., 1958. A note on the fundamental identity of sequential analysis. Annals of Mathematical Statistics 29 534–543.
BELLMAN, RICHARD, 1952. On the theory of dynamic programming. Proceedings of the National Academy of Sciences of the United States of America 38 716–719.
BELLMAN, RICHARD, 1956. A problem in the sequential design of experiments. Sankhyā 16 221–229.
BELLMAN, RICHARD, 1957. Dynamic Programming. Princeton University Press, Princeton, New Jersey.
BERNOULLI, JACOB (James), 1713. Ars conjectandi. Thurnisius Brothers, Basel.
BERTRAND, J., 1907. Calcul des Probabilités, second edition. Gauthier-Villars, Paris.
BLACKWELL, DAVID, 1946. On an equation of Wald. Annals of Mathematical Statistics 17 84–87.
BLACKWELL, DAVID, 1954. On optimal systems. Annals of Mathematical Statistics 25 394–397.
BLACKWELL, DAVID, 1964. Probability bounds via dynamic programming. Proceedings of Symposia in Applied Mathematics, American Mathematical Society, Providence, Rhode Island, XVI 277–280.
BREIMAN, LEO, 1961. Optimal gambling systems for favorable games. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, California, 1 65–78.
CHUNG, K. L., and W. H. J. FUCHS, 1951. On the distribution of sums of random variables. Memoirs of the American Mathematical Society 6 1–12.
COOLIDGE, J. L., 1908–1909. The gambler’s ruin. Annals of Mathematics 10 181–192.
DE FINETTI, BRUNO, 1930. Sulla proprietá conglomerativa delle probabilitá subordinate. Rendiconti dell’Istituto Lombardo 63 414–418.
DE FINETTI, BRUNO, 1937. La prévision: ses lois logiques, ses sources sub-jectives. Annals de l’Institut Henri Poincare 7 1–68.
DE FINETTI, BRUNO, 1939. La teoria del rischio e il problema della “rovina dei giocatori”. Giornale dell’Istituto Italiano degli Attuari 10 41–51.
DE FINETTI, BRUNO, 1940. Il problema dei “pieni”. Giornale dell’Istituto Italiano degli Attuari 11 1–88.
DE FINETTI, BRUNO, 1949. Sull impostazione assiomatica del calcolo delle probability. Annali Triestini 19 29–81.
DE FINETTI, BRUNO, 1950. Aggiunta alla nota sull’assiomatica della probabilitá. Annali Triestini 20 [Series 4, Volume 4, second section (science and engineering)] 5–22.
DE FINETTI, BRUNO, 1955. La struttura delle distribuzione in un insieme astratto qualsiasi. Giornale dell’Istituto Italiano degli Attuari 18 16–28.
DE FINETTI, BRUNO, 1955a. Sulla teoria astratta della misura e dell’integrazione. Annate di matematica pura ed applicata (Serie IV) 40 307–319.
DE MOIVRE, ABRAHAM, 1711. De mensura sortis. Philosophical Transactions 27 213–264.
DE MOIVRE, ABRAHAM, 1718. The Doctrine of Chances. Printed for the author by W. Pearson, London.
DE RHAM, GEORGES, 1956–1957. Sur quelques courbes definies par des équations fonctionelles. Rendiconti del Seminario Matematico dell’Università e del Politecnico di Torino 16 101–113.
DERMAN, C, and H. ROBBINS, 1955. The strong law of large numbers when the first moment does not exist. Proceedings of the National Academy of Sciences of the United States of America 41 586–587.
DESCARTES, RENÉ, 1925. Livre troisième, la geometrie. The Geometry of René Descartes. Translated by David Eugene Smith and Marcia L. Latham. The Open Court Publishing Company, Chicago, Illinois; London.
DICKSON, LEONARD EUGENE, 1939. New First Course in the Theory of Equations. John Wiley & Sons, Inc., New York.
DIEUDONNÉ, J., 1960. Foundations of Modern Analysis. Academic Press Inc.. New York.
DOOB, J. L., 1953. Stochastic Processes. John Wiley & Sons, Inc., New York.
DUBINS, LESTER E., 1962. Rises and upcrossings of nonnegative martingales. Illinois Journal of Mathematics 6 226–241.
DUBINS, LESTER E., and DAVID A. FREEDMAN, 1965. A sharper form of the Borel-Cantelli lemma and the strong law. Annals of Mathematical Statistics 36 800–807.
DUBINS, LESTER E., and LEONARD J. SAVAGE, 1960. How to Gamble If You Must. Privately circulated.
DUBINS, LESTER E., and LEONARD J. SAVAGE, 1960a. Optimal gambling systems. Proceedings of the National Academy of Sciences of the United States of America 46 1597–1598.
DUBINS, LESTER E., and LEONARD J. SAVAGE, 1963. How to Gamble If You Must: Inequalities for Stochastic Processes. Privately circulated.
DUBINS, LESTER E., and LEONARD J. SAVAGE, 1965. A Tchebycheff-like inequality for stochastic processes. Proceedings of the National Academy of Sciences of the United States of America 51 274–275.
DUNFORD, NELSON, and JACOB T. SCHWARTZ, 1958. Linear Operators, Part I: General Theory. Interscience Publishers, Inc., New York.
FELDMAN, DORIAN, 1962. Contributions to the “two-armed bandit problem”. Annals of Mathematical Statistics 33 847–856.
FELLER, WILLIAM, 1950. An Introduction to Probability Theory and Its Applications, Volume I. John Wiley & Sons, Inc., New York.
GNEDENKO, B. V., and A. N. KOLMOGOROV, 1954. Limit Distributions for Sums of Random Variables. Translated by K. L. Chung. Addison-Wesley Publishing Company, Inc., Reading, Massachusetts.
GIRSHICK, M. A., and L. J. SAVAGE, 1951. Bayes and minimax estimates for quadratic loss functions. Proceedings of the Second [1950] Berkeley Symposium on Mathematical Statistics and Probability. Edited by Jerzy Neyman. University of California Press, Berkeley, California, 53–74.
HALMOS, P. R., 1939. Invariants of certain stochastic transformations: The mathematical theory of gambling systems. Duke Mathematical Journal 5 461–478.
HARDY, G. H., J. E. LITTLEWOOD, and G. POLYA, 1934. Inequalities. Cambridge University Press, New York and London. (Second, similar edition 1954.)
HAUSDORFF, FELIX, 1957. Set Theory. Chelsea Publishing Company, New York.
HEWITT, EDWIN, 1960. Integration by parts for Stieljes integrals. American Mathematical Monthly 67 419–423.
HILLE, EINAR, and RALPH S. PHILLIPS, 1957. Functional Analysis and Semigroups, revised edition. American Mathematical Society, Providence, Rhode Island.
HOEFFDING, WASSILY, 1963. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58 13–30.
HOWARD, RONALD A., 1961. Dynamic Programming and Markov Processes. John Wiley & Sons, Inc., New York.
HUNT, G. A., 1957. Markov processes and potentials, I. Illinois Journal of Mathematics 1 44–93.
KALMÁR, L., 1957. Über arithmetische Funktionen von unendlich vielen Variablen, welche an jeder Stelle bloss von einer endlichen Anzahl von Variablen abhängig sind. Colloquium Mathematicum 5 1–5.
KALIN, SAMUEL, 1955. The structure of dynamic programing models. Naval Research Logistics Quarterly 2 285–294.
KELLEY, JOHN L., 1955. General Topology, D. Van Nostrand Company, Inc., Princeton, New Jersey.
KEMPERMAN, J. H. B., 1961. The Passage Problem for a Stationary Markov Chain. The University of Chicago Press, Chicago.
KÖNIG, DENES, 1936. Theorie der endlichen und undendlichen Graphen. Akademische Verlagsgesellschaft, Leipzig.
KRUSKAL, JOSEPH B., 1963. The number of simplices in a complex. Chapter 12, Mathematical Optimization Techniques, edited by Richard Bellman. Report R-366-PR, RAND Corporation, Santa Monica, California.
KURATOWSKI, CASIMIR, 1932. Les fonctions semi-continues dans I’espace des ensembles fermés. Fundamenta Mathematicae 18 148–159.
LEHMER, DERRICK H., 1964. The machine tools of combinatories. Chapter 1, Combinatorial Analysis for Engineers and Scientists, edited by Edwin F. Beckenbach. John Wiley & Sons, Inc., New York.
LÉVY, PAUL, 1937. Théorie de l’Addition des Variables Aléatoires. Gauthier-Villars, Paris. (Second edition 1954.)
LIAPUNOV, A. A., E. A. SCHEGOLKOW, and W. J. ARSENIN, 1955. Arbeiten zur deskriptiven Mengenlehre. Deutches Verlag der Wissenschaften, Berlin.
LOEVE, MICHEL, 1955. Probability Theory. D. Van Nostrand Company, Inc., Princeton, New Jersey.
LUSIN, NICOLAS, 1930. Leçons sur les ensembles analytiques et leurs applications. Gauthier-Villars, Paris.
RAIFFA, HOWARD, and ROBERT SCHLAIFER, 1961. Applied Statistical Decision Theory. Graduate School of Business Administration, Harvard University, Boston, Massachusetts.
RAOULT, J. P., 1964. Sur une notion de fonction universellement intégrable introduite par Dubins et Savage. Publications de l’Institut de Statistiques de l’Universite de Paris 13 79–108.
RAOULT, J. P., 1964a. Résultats récents de Savage et Dubins sur les paris. Bulletin de l’Institut des Actuaires Frangais 247 65–83.
RILEY, J. A., and THEODORE HATCHER, 1958. Problem E 1288. American Mathematical Monthly 65 368.
RILEY, J. A., and THEODORE HATCHER, 1959. Problem 4858. American Mathematical Monthly 66 595.
ROBBINS, HERBERT, 1952. Some aspects of the sequential design of experiments. Bulletin of the American Mathematical Society 58 527–535.
ROSENBLATT, MURRAY, 1962. Random Processes. Oxford University Press, New York.
SAKS, STANISLAW, 1932. Theory of the Integral, second revised edition. Fundusz Kultury Narodowej, Warsaw.
SAVAGE, LEONARD J., 1954. The Foundations of Statistics, John Wiley & Sons, Inc., New York.
SAVAGE, LEONARD J., 1957. The casino that takes a percentage and what you can do about it. Unpublished report P-1132, RAND Corporation, Santa Monica, California (July 1957, revised October 17).
SAVAGE, LEONARD J., 1962. Bayesian statistics, Decision and Information Processes. Edited by R. Machol and P. Gray. The Macmillan Company, New York, 161–194.
SCARNE, JOHN, 1961. Scarne’s Complete Guide to Gambling. Simon and Schuster, Inc., New York.
SIERPINSKI, W., 1950. Les ensembles projectifs et analytiques. Memorial des sciences mathematiques 112 1–80.
SPITZER, FRANK, 1956. A combinatorial lemma and its application to probability theory. Transactions of the American Mathematical Society 82 323–339.
TODHUNTER, I., 1865. A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace. The Macmillan Company, Cambridge and London. (Reprinted by Chelsea Publishing Company, New York, 1949.)
WALD, ABRAHAM, 1947. Sequential Analysis. John Wiley & Sons, Inc., New York.
WALD, ABRAHAM, 1950. Statistical Decision Functions. John Wiley & Sons, Inc., New York.
WALD, A., and J. WOLFOWITZ, 1948. Optimum character of the sequential probability ratio test. Annals of Mathematical Statistics 19 326–339.
WEINGARTEN, HARRY, 1956. On the probability of large deviations of bounded chance variables. Annals of Mathematical Statistics 27 1170–1174.
WIDDER, D. V., 1941. The Laplace Transform. Princeton University Press, Princeton, New Jersey.