2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103650$μ$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $ν=e^{-2F} μ$ to also satisfy some log-Sobolev inequality. Explicit examples are studied.ProbabilityMSC 47D07, 60E15, 60G10text