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Limit Points of Bernoulli Distribution Algebras Induced by Boolean Functions

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Abstract

We consider Bernoulli distribution algebras, i.e. sets of distributions that are closed under transformations achieved by substituting independent random variables for arguments of Boolean functions from a given system. We establish that, unless the transforming set contains only essentially unary functions, the set of algebra limit points is either empty, single-element or no less than countable.

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Acknowledgments

The author expresses gratitude to O.M. Kasim-Zade for his attention to the present work.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Moscow, 125047, Russia

    A. D. Yashunsky

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  1. A. D. Yashunsky
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Correspondence to A. D. Yashunsky.

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Yashunsky, A.D. Limit Points of Bernoulli Distribution Algebras Induced by Boolean Functions. Lobachevskii J Math 40, 1423–1432 (2019). https://doi.org/10.1134/S199508021909021X

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  • DOI: https://doi.org/10.1134/S199508021909021X

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