Kantorovich's Mass Transport Problem for Capacities

Abstract

The aim of the present paper is to extend Kantorovich's mass transport problem to the framework of upper/lower continuous capacities and to prove the cyclic monotonicity of the supports of optimal supermodular plans. As in the probabilistic case, this easily yields the corresponding extension of the Kantorovich duality.

This is the final version, as it is published in the journal. With respect to the previous version, on page 4 it was modified the definition of Choquet integral on a set A