2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221583We prove an isoperimetric inequality for probability measures $μ$ on $\mathbb{R}^n$ with density proportional to $\exp(-ϕ(λ| x|))$, where $|x|$ is the euclidean norm on $\mathbb{R}^n$ and $ϕ$ is a non-decreasing convex function. It applies in particular when $ϕ(x)=x^α$ with $α\ge1$. Under mild assumptions on $ϕ$, the inequality is dimension-free if $λ$ is chosen such that the covariance of $μ$ is the identity.Probability26D10, 60E15, 28A75text