  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.
