A new characterization of Talagrand’s transportentropy inequalities and applications

Abstract. We give a characterization of transport-entropy inequalities in met-ric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley-Stroock perturbation Lemma). 1. Introduction. In their celebrated paper [24], Otto and Villani proved that, in a smooth Rie-mannian setting, the log-Sobolev inequality implies the Talagrand’s transport-ent-ropy inequality T2. Later, Bobkov, Gentil and Ledoux [3] proposed an alternative proof of this result. Both approaches are based on semi-group arguments. Mor