LOG-CONCAVE MEASURESD. FEYEL, A. S.USTUNEL (pp. 92-105)
We study the log-concave measures, their characterization via the Pr ́ekopa-Leindlerproperty and also define a subset of it whose elements are called super log-concave measureswhich have the property of satisfying a logarithmic Sobolev inequality. We give some resultsabout their stability. Certain relations with measure transportation are also indicated.
Log-concave measures, logarithmic Sobolev inequality, measure transport, Pr ́kopa-Leindler inequality,H-convexity.