On the improvement of concavity of convex measures

Abstract

We prove that a general class of measures, which includes $\log$-concave measures, is $\frac{1}{n}$-concave according to the terminology of Borell, with additional assumptions on the measures or on the sets, such as symmetries. This generalizes results of Gardner and Zvavitch.

arXiv commentCorrected typos, 14 pages

References in corpus (1)

• On some inequalities for Gaussian measures