Mathematics

A general class of functionals which measure the cost of a path in a metric space joining two given points is considered and abstract existence results for optimal paths are provided. The results are then applied to the case the metric space is a Wasserstein space of probabilities on a given subset of the Euclidean space and the cost of a path depends on the value of classical functionals over measures, providing a model of mass transportation different from the classical Monge-Kantorovich theory.