We consider the transformations of independent random variables over a linearly ordered finite set (a chain) by the join and meet operations. We investigate the possibility of approximating an arbitrary probability distribution on a chain by means of a (possibly iterated) application of the join and meet operations to independent random variables with distributions from a given set. We establish some conditions under which the approximation is impossible and the conditions when it becomes possible.
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The author is grateful to O. M. Kasim-Zade for his attention to this study.
Translated by Ya.A. Kopylov
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Yashunsky, A.D. On the Approximation of Random Variables on a Finite Chain. J. Appl. Ind. Math. 14, 581–591 (2020). https://doi.org/10.1134/S1990478920030163