2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140867We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on $\dR^n$, with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality for all uniform strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.Probabilitytext