Interval distribution function of a bounded chaotic sequence as a basis of nonaxiomatic probability theory

Abstract

We introduce the notion of interval distribution function of random events on the set of elementary events and the notion of interval function of the frequencies of these events. In the limiting case, the interval function turns into the ordinary distribution function and the interval function of frequencies (under certain conditions) turns into the density of distribution of random events. The case of discrete sets of elementary events is also covered. This enables one to introduce the notion of the probability of occurrence of random events as a result of the limit transition.