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On the Regularities of Mass Random Phenomena

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Continuous and Distributed Systems

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 211))

Abstract

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.

Valery A. Labkovsky—deceased.

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Notes

  1. 1.

    Remark that the term “nonstochastic” appeared in [27] in the context of Kolmogorov’s complexity, meaning “more complex than stochastic”. In this chapter the meaning of this term is “more random than stochastic”.

  2. 2.

    I am thankful to professor Vladimir Vovk who made me familiar with the works of professor Terrence Fine and, in particular, with this chapter.

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Authors and Affiliations

  1. Kyiv Polytechnical Institute, Prospekt Peremogy, 37, Kyiv, 03056, Ukraine

    Victor I. Ivanenko

  2. Mechanics and Mathematics Department, Moscow State University, Moscow, Russia

    Valery A. Labkovsky

Authors
  1. Victor I. Ivanenko
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  2. Valery A. Labkovsky
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Correspondence to Victor I. Ivanenko .

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Editors and Affiliations

  1. National Academy of Science, National Technical University of Ukraine, Kiev, Ukraine

    Mikhail Z. Zgurovsky

  2. Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

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Ivanenko, V.I., Labkovsky, V.A. (2014). On the Regularities of Mass Random Phenomena. In: Zgurovsky, M., Sadovnichiy, V. (eds) Continuous and Distributed Systems. Solid Mechanics and Its Applications, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-03146-0_17

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  • DOI: https://doi.org/10.1007/978-3-319-03146-0_17

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