2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77569Final representation of all those measures $μ$ for which algebraic polynomials are dense in $L_p(R, dμ)$ 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.LaTeX, amsfonts, 45 pClassical Analysis and ODEs41A10; 30D10;30D45text