Khrennikov, A. Yu. - p-adic theory of probability and its applications. A principle of the statistical stabilization of frequencies. Teor. and Matem. Fiz., 97, No. 3, 348--363 (1993).  Home/Search   Document Not in Database   Summary   Related Articles

....6, 1998 1 Introduction The development of a non Archimedean (especially, p adic) mathematical physics [20] 22] 1] 4] 6] 8] 13] induced some new mathematical structures over non Archimedean fields. In particular, probability theory with p adic valued probabilities was developed in [11], 8] 4] 1 . The first theory with p adic probabilities was the frequency theory in which probabilities were defined as limits of relative frequencies N = n=N in the p adic topology 2 .This frequency probability theory was a natural extension of the frequency probability theory of R. von ....

....measure theoretical axiomatics of probability theory. Kolmogorov used properties of the frequency probability (non negativity, normalization by 1 and additivity) as the basis of his axiomatics. Then he added the technical condition of oe additivity for using Lebesgue s integration theory. In works [11], 8] we tried to follow A.N. Kolmogorov. p adic frequency probability has also the properties of additivity, it is normalized by 1 and the set of possible values of this probability is the whole field of p adic numbers Q p : Thus it was natural to define p adic probability as a Q p valued ....

Khrennikov, A. Yu. - p-adic theory of probability and its applications. A principle of the statistical stabilization of frequencies. Teor. and Matem. Fiz., 97, No. 3, 348--363 (1993).

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