2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140205We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces $L_X^p$, where $X$ is a Banach space and $1\le p<\infty$, and extend the result to vector-valued Banach function spaces $E_X$, where $E$ is a Banach function space with order continuous norm.6 pagesFunctional Analysis46E40text