Geodesic
A~limit theorem for $p$-adic-valued probability distributions
Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 647-662.

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Probability models in which probabilities, defined in the sense of von Mises as limits of relative frequencies, can belong to $p$-adic number fields appeared in connection with the problem of the probabilistic interpretation of wave functions in $p$-adic-valued quantum mechanics and field theory. Here we present a variant of axiomatic $p$-adic probability theory in the framework of the theory of analytic distributions on $p$-adic spaces. We prove a theorem on the existence of $p$-adic-valued probability distributions on $p$-adic sequences and obtain a limit theorem for sums of independent random variables (an analogue of the law of large numbers). 
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A. Yu. Khrennikov. A~limit theorem for $p$-adic-valued probability distributions. Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 647-662. http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a7/

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