The Existence of Probability Measures with Given Marginals

Abstract

In an important paper, Strassen discussed the existence of measures on product spaces with given marginals in the context of Polish spaces. We generalize his results to arbitrary Hausdorff spaces and indicate some applications such as measures with given support and stochastic inequalities on partially ordered Hausdorff spaces. In the second part of our paper, we state two results on the general moment problem, thus generalizing earlier theorems due to Kemperman.