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On necessary conditions of probability limit theorems in finite algebras
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 47-50 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the conditions for a finite set with a given system of operations (a finite algebra) to be subject to a probability limit theorem, i.e., arbitrary computations with mutually independent random variables have value distributions that tend to a certain limit (limit law) as the number of random variables used in the computation grows. Such behavior may be seen as a generalization of the central limit theorem that holds for sums of continuous random variables. We show that the existence of a limit probability law in a finite algebra has strong implications for its set of operations. In particular, with some geometric exceptions excluded, the existence of a limit law without zero components implies that all operations in the algebra are quasigroup operations and the limit law is uniform.
Keywords: finite algebra, random variable, limit theorem, uniform distribution.
Mots-clés : quasigroup 
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A. D. Yashunskii. On necessary conditions of probability limit theorems in finite algebras. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 47-50. http://geodesic.mathdoc.fr/item/DANMA_2020_493_a9/

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