p-Adic probability theory and its applications. The principle of statistical stabilization of frequencies

The development ofp-adic quantum mechanics has made it necessary to construct a probability theory in which the probabilities of events arep-adic numbers. The foundations of this theory are developed here. The frequency definition of probability is used. A general principle of statistical stabilization of relative frequencies is formulated. By virtue of this principle, statistical stabilization of relative frequencies, which are, like all experimental data, rational numbers, can be considered not only in the real topology but also inp-adic topologies.Institute of Electronic Technology, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 3, pp. 348–363, December, 1993.