Inserted: 14 sep 2009
Last Updated: 6 aug 2010
Journal: Manuscripta Math.
We study a new class of distances between Radon measures similar to those studied in a recent paper of Dolbeault-Nazaret-Savaré DNS. These distances (more correctly pseudo-distances because can assume the value $+\infty$) are defined generalizing the dynamical formulation of the Wasserstein distance by means of a concave mobility function. We are mainly interested in the physical interesting case (not considered in DNS) of a concave mobility function defined in a bounded interval. We state the basic properties of the space of measures endowed with this pseudo-distance. Finally, we study in detail two cases: the set of measures defined in $R^d$ with finite moments and the set of measures defined in a bounded convex set. In the two cases we give sufficient conditions for the convergence of sequences with respect to the distance and we prove a property of boundedness.
Keywords: generalized Wasserstein distance, mobility function