We prove a version for randommeasures of the celebrated KantorovichRubinštein duality theorem and we give an application to the coupling of random variables which extends and unifies known results. Résumé Nous démontrons une version du théorème de dualité de KantorovichRubinštein pour les mesures aléatoires, et nous donnons une application au couplage des variables aléatoires qui étend et unifi...

We show that, for the space of Borel probability measures on a Borel subset of a Polish metric space, the extreme points of the Prokhorov, Monge-Wasserstein and Kantorovich metric balls about a measure whose support has at most n points, consist of measures whose supports have at most n+2 points. Moreover, we use the Strassen and Kantorovich-Rubinstein duality theorems to develop representation...

This note contains three versions of a result which is sometimes referred to as Kneser’s lemma and states that (with respect to a fixed triangulation) there is a bound on the number of disjointly embedded normal surfaces in a 3–manifold which satisfy an extra non–triviality condition. One often stipulates that no two of the surfaces be parallel in M . We relax this condition and merely assume t...

Lenses and quasi-lenses on a space X form models of erratic non-determinism. When is equipped with quasi-metric d, there are natural quasi-metrics dP dPa the X, which resemble Pompeiu-Hausdorff metric (and contain it as subcase when d metric), tightly connected to Kantorovich-Rubinstein dKR dKRa Parts I, II III, through an isomorphism between so-called discrete normalized forks. We show that co...