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.

中文翻译：

---

有限值随机变量代数逼近的必要条件

摘要

我们考虑通过代数运算对有限集上的随机变量进行转换。如果可以通过将给定的运算应用于分布不为零的相互独立的相同分布的随机变量来以任意精度近似任意随机变量，则该运算系统被称为近似完整。我们为函数系统近似逼近建立了一些必要条件，并构造了近似不完整系统的实例。