On Necessary Conditions of Finite-Valued Random Variable Algebraic Approximation

Abstract

We consider transformations of random variables on finite sets by algebraic operations. A system of operations is said to be approximation complete if any random variable may be approximated with arbitrary precision by applying the given operations to mutually independent identically distributed random variables whose distributions have no zero components. We establish some necessary conditions for a function system to be approximation complete and construct examples of approximation incomplete systems.