×
Rényi, Alfréd

On a new axiomatic theory of probability. (English) Zbl 0067.10401

Acta Math. Acad. Sci. Hung. 6, 285-335 (1955).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0067.10401

Cited in 6 Reviews
Cited in 144 Documents

Keywords:

probability theory
Cite Review PDF
Full Text: DOI

References:

[1] A. N. Kolmogoroff,Grundbegriffe der Wahrscheinlichkeitsrechnung (Berlin, 1933). · Zbl 0007.21601
[2] H. Jeffreys,Theory of probability (London, 1943). · Zbl 0023.14501
[3] H. Reichenbach,Wahrscheinlichkeitslehre (Leiden, 1935).
[4] M. I. Keynes,A treatise on probability theory.
[5] B. O. Koopman, The axioms and algebra of intuitive probability,Annals of Math.,41 (1940), pp. 269–292. · Zbl 0024.05001 · doi:10.2307/1969003
[6] A. H. Copeland, Postulates for the theory of probability,Amer. Journal of Math.,63 (1941), pp. 741–762. · Zbl 0026.13605 · doi:10.2307/2371618
[7] G. A. Barnard, Statistical inference,Journal of the Royal Statistical Soc., Ser. B,11 (1949), pp. 115–139. · Zbl 0039.35401
[8] I. J. Good,Probability and the weighing of evidence (London, 1950). · Zbl 0036.08402
[9] A. Rényi, A valószínuségszámítas új axiomatikus felépítése,MTA Mat. és Fiz. Oszt. Közl.,4 (1954), pp. 369–427.
[10] 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.
[11] A. Rényi, Über die axiomatische Begründung der Wahrscheinlichkeitsrechnung. Under press in theProceedings of the Conference on Probability Theory in Berlin, 1954.
[12] J. Hájek andA. Rényi, Generalization of an inequality of Kolmogorov,Acta Math. Acad. Sci. Hung.,6 (1955), pp. 281–283. · Zbl 0067.10701 · doi:10.1007/BF02024392
[13] Á. Császár, Sur la structure des espaces de probabilité conditionnelle,Acta Math. Acad. Sci. Hung.,6 (1955), pp. 337–361. · Zbl 0067.10402 · doi:10.1007/BF02024394
[14] J. Neyman, L’estimation statistique traitéc comme un problème classique de probabilité,Act. Sci. et Ind., 739 (Paris, 1938), pp. 25–57.
[15] P. Halmos,Measure theory (New-York, 1951). · Zbl 0045.05702
[16] P. Erdös, On the integers having exactlyk prime factors,Annals of Math.,49 (1948), pp. 53–66. · Zbl 0030.29604 · doi:10.2307/1969113
[17] B. V. Gnedenko, Über ein lokales Grenzwerttheorem für gleichverteilte unabhängige Summanden,Wiss. Zeitschrift der Humboldt-Universität Berlin,3 (1954), pp. 287–293. · Zbl 0059.12401
[18] J. L. Doob,Stochastic processes (New-York, 1953). · Zbl 0053.26802
[19] C. Derman, A solution to a set of fundamental equations in Markov chains,Proc. Amer. Math. Soc.,5 (1954), pp. 332–334. · Zbl 0058.34504 · doi:10.1090/S0002-9939-1954-0060757-0
[20] Erdos P. andK. L. Chung, Probability limit theorems assuming only the first moment. I,Memoirs of the Amer. Math. Soc.,6 (1952).
[21] 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. · doi:10.1090/S0002-9947-1954-0063603-9
[22] 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. · Zbl 0026.23001 · doi:10.1214/aoms/1177731708
[23] L. Takács, Egy új módszer rekurrens sztochasztikus folyamatok tárgyalásánál,MTA Alk. Mat. Int. Közleményei,2 (1953), pp. 135–163.
[24] O. Perron Irrationalzahlen (Berlin, 1921), pp. 111–116.
[25] E. Borel, Les probabilités dénombrables et leurs applications arithmétiquesRend. Circ. Math. Palermo,27 (1909), pp. 247–271. · JFM 40.0283.01 · doi:10.1007/BF03019651
[26] H. Hahn andA. Rosenthal, Set functions (New Mexico, 1948). · Zbl 0033.05301
[27] M. Loève,Probability theory (New-York, 1955).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.