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math.ST updates on arXiv.org

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On regularities of mass random phenomena
Victor I. Ivanenko, Valery A. Labkovsky · 2012-04-20 · via math.ST updates on arXiv.org

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.

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