On the Regularities of Mass Random Phenomena

By V. Ivanenko, V. A. Labkovsky. 2012

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This note presents a not very well known result concerning the frequentist origins of probability. This result provides a positive answer to the question of existence of statistical regularities of so called random in a broad sense mass phenomena, using the terminology of A. N. Kolmogorov [20]. It turns out, that some closed in weak-\(*\) topology family of finitely-additive probabilities plays the role of the statistical regularity of any such phenomenon. If the mass phenomenon is stochastic, then this family degenerates into a usual countably-additive probability measure. The note provides precise definitions, the formulation and the proof of the theorem of existence of statistical regularities, as well as the examples of their application.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/38deed2d7c1d7e991415b51115c781825d92b067