Algebras of Probability Distributions on Finite Sets

Abstract

We consider the problems of transforming random variables over finite sets by discrete functions. We describe the problems of exact and approximate expression of random variables as functions of other random variables from the point of view of universal algebra and provide a review of results in the area. Sufficient conditions are obtained for a system of transforming functions to allow the approximation of an arbitrary probability distribution on a finite set using a given nondegenerate initial distribution.