On Approximation of Random Variables

The article deals with the best approximation of a random variable by a set of random variables. Approximation by means of linear combinations of the above set is rather common. In the article this approach is extended to use of polynomial functions of this set elements. If degrees of polynomials are arbitrary then it results in approximation by means of a conditional mathematical expectation of a random variable concerning this set. Linear spaces of random variables are described in which the specified methods of approximation result in the same result.

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