Polynomial approximation in $L_p(R, d\mu)$. I

Abstract

Final representation of all those measures $\mu$ for which algebraic polynomials are dense in $L_p(R, d\mu)$ is found. The weighted analogue of the Weierstrass polynomial approximation theorem and a new version of the M. Krein's theorem about partial fraction decomposition of reciprocal of an entire function are established.