Statistical regularities of mass phenomena

The paper addresses the issue of frequentist origins of probability and provides a positive answer to the question of existence of regularities of so called random in a broad sense mass phenomena [1]. It turns out that some closed in *-weak topology family of finitely-additive probability measures corresponds to any such phenomenon as its statistical regularity. If the mass phenomenon is stochastic (that is, statistically stable), then this family degenerates into a usual unique probability measure. The article provides precise definitions, the statement and proof of the theorem of existence of statistical regularities, and examples where there is a need in families of finitely-additive probability measures.