On regularities of mass random phenomena

TL;DR

This paper investigates the existence of regularities in broad-sense random phenomena, showing that finitely-additive probabilities serve as their statistical regularities, which simplify to a single measure in stochastic cases.

Contribution

It establishes the existence of statistical regularities for broad-sense random phenomena and characterizes their form as finitely-additive probabilities, with proofs and applications.

Findings

Finitely-additive probabilities are the statistical regularities of broad-sense random phenomena.

In stochastic cases, these probabilities reduce to a single probability measure.

The paper provides formal definitions, theorems, and examples of applications.

Abstract

This paper contains an answer to the question of existence of regularities of the so called \textit{random in a broad sense} mass phenomena, asked by A. N. Kolmogorov in \cite{Kolmogorov}. It turns out that some family of finitely-additive probabilities is the statistical regularity of any such phenomenon. If the mass phenomenon is stochastic, then this family degenerates into a single probability measure. The paper provides definitions, the formulation and the proof of the theorem of existence of statistical regularities, as well as the examples of their application.