This is a preview of subscription content, log in via an institution to check access.
Bibliography
A. N. Kolmogoroff,Grundbegriffe der Wahrscheinlichkeitsrechnung (Berlin, 1933).
H. Jeffreys,Theory of probability (London, 1943).
H. Reichenbach,Wahrscheinlichkeitslehre (Leiden, 1935).
M. I. Keynes,A treatise on probability theory.
B. O. Koopman, The axioms and algebra of intuitive probability,Annals of Math.,41 (1940), pp. 269–292.
A. H. Copeland, Postulates for the theory of probability,Amer. Journal of Math.,63 (1941), pp. 741–762.
G. A. Barnard, Statistical inference,Journal of the Royal Statistical Soc., Ser. B,11 (1949), pp. 115–139.
I. J. Good,Probability and the weighing of evidence (London, 1950).
A. Rényi, A valószínűségszámítas új axiomatikus felépítése,MTA Mat. és Fiz. Oszt. Közl.,4 (1954), pp. 369–427.
A. Rényi, On a new axiomatic foundation of the theory of probability. Under press in the Volume 1 of theProceedings of the International Mathematical Congress in Amsterdam, 1954.
A. Rényi, Über die axiomatische Begründung der Wahrscheinlichkeitsrechnung. Under press in theProceedings of the Conference on Probability Theory in Berlin, 1954.
J. Hájek andA. Rényi, Generalization of an inequality of Kolmogorov,Acta Math. Acad. Sci. Hung.,6 (1955), pp. 281–283.
Á. Császár, Sur la structure des espaces de probabilité conditionnelle,Acta Math. Acad. Sci. Hung.,6 (1955), pp. 337–361.
J. Neyman, L'estimation statistique traitéc comme un problème classique de probabilité,Act. Sci. et Ind., 739 (Paris, 1938), pp. 25–57.
P. Halmos,Measure theory (New-York, 1951).
P. Erdös, On the integers having exactlyk prime factors,Annals of Math.,49 (1948), pp. 53–66.
B. V. Gnedenko, Über ein lokales Grenzwerttheorem für gleichverteilte unabhängige Summanden,Wiss. Zeitschrift der Humboldt-Universität Berlin,3 (1954), pp. 287–293.
J. L. Doob,Stochastic processes (New-York, 1953).
C. Derman, A solution to a set of fundamental equations in Markov chains,Proc. Amer. Math. Soc.,5 (1954), pp. 332–334.
Erdős P. andK. L. Chung, Probability limit theorems assuming only the first moment. I,Memoirs of the Amer. Math. Soc.,6 (1952).
K. L. Chung, Contributions to the theory of Markov chains,Trans. Amer. Math. Soc.,76 (1954), pp. 397–419. See alsoK. L. Chung, An ergodic theorem for stationary Markov chains with a countable number of states,Proc. Internat. Congress of Math. Cambridge (USA), 1950, (Amer. Math. Soc., 1952), I, p. 568.
W. Feller, On the integral equation of renewal theory,Ann. Math. Stat.,12 (1941), pp. 243–267. See alsoS. Täcklind, Elementare Behandlung vom Erneuerungsproblem,Skandinavisk Aktuarietidskrift, (1944), pp. 1–15, and Fourier-analytische Behandlung vom Erneuerungsproblem,Skandinavisk Aktuarietidskrift, (1945), pp. 101–105; andJ. L. Doob, Renewal theory from the point of view of the theory of probability,Trans. Amer. Math. Soc.,63 (1948), pp. 422–438.
L. Takács, Egy új módszer rekurrens sztochasztikus folyamatok tárgyalásánál,MTA Alk. Mat. Int. Közleményei,2 (1953), pp. 135–163.
O. Perron Irrationalzahlen (Berlin, 1921), pp. 111–116.
E. Borel, Les probabilités dénombrables et leurs applications arithmétiquesRend. Circ. Math. Palermo,27 (1909), pp. 247–271.
H. Hahn andA. Rosenthal, Set functions (New Mexico, 1948).
M. Loève,Probability theory (New-York, 1955).
Author information
Authors and Affiliations
Additional information
Dedicated to Professors L. Fejér and F. Riesz on their 75 th birthday
Rights and permissions
About this article
Cite this article
Rényi, A. On a new axiomatic theory of probability. Acta Mathematica Academiae Scientiarum Hungaricae 6, 285–335 (1955). https://doi.org/10.1007/BF02024393
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02024393