On the Role of Cylindrical Functions in Kantorovich duality

Abstract

We study the dual formulation of the Monge-Kantorovich optimal transportation problem, in particular under what circumstances it is permitted in an infinite dimensional setting to use cylindrical functions, i.e. functions of the form $\phi \circ P$ where $P$ is a finite-rank operator and $\phi$ is a smooth, compactly supported function. In the last section, some examples of applications are presented.