Duality theorems for marginal problems

Abstract

Given topological spaces X1, ..., Xn with product space X, probability measures μi on Xi together with a real function h on X define a marginal problem as well as a dual problem. Using an extended version of Choquet's theorem on capacities, an analogue of the classical duality theorem of linear programming is established, imposing only weak conditions on the topology of the spaces Xi and the measurability resp. boundedness of the function h. Applications concern, among others, measures with given support, stochastic order and general marginal problems. © 1984 Springer-Verlag.