TWO WAYS TO DEFINE COMPATIBLE METRICS ON THE SIMPLEX OF MEASURES

摘要

We introduce two general methods of lifting a metric on a space to the simplex of probability measures on this space. The first one is the method of transportation plans, or the coupling method; the second one consists in considering norms dual to the restrictions of the Lipschitz norm to subspaces. The intersection of the corresponding two classes of metrics consists of the Kantorovich metric.