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\(p\)-adic probability and statistics. (English. Russian original) Zbl 0768.60002
Sov. Phys., Dokl. 37, No. 2, 81-83 (1992); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 322, No. 6, 1075-1079 (1992).
The foundations of a new theory of probability are laid. A general principle is proposed for statistical stabilization of the relative frequency of events. Using this principle, the statistical stabilization of the relative frequencies can be investigated not only in the real topology over the field of natural numbers, but also in other topologies and, in particular, in \(p\)-adic topologies, although it must be emphasized that relative frequencies always belong to the field of rational numbers \(Q\). There arises a whole spectrum of new theories, in which each topology of statistical stabilization corresponds to its own theory of probability. The probability of events then belongs to the completion of the field of rational numbers that results from a given statistical stabilization topology.

MSC:
60A99 Foundations of probability theory
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