2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160434In this paper we study the set of functions $\GG$-valued which can be approximated by $\GG$-valued continuous functions in the norm $L^\infty_{\GG}(I,w)$, where $I$ is a compact interval, $\GG$ is a real and separable Hilbert space and $w$ is certain $\GG$-valued weakly measurable weight. Thus, we obtain a new extension of celebrated Weierstrass approximation theorem.Corrected version, 14 pagesClassical Analysis and ODEsFunctional Analysis41, 41A10, 43A32, 47A56text