On exchangeability and Hausdorff moment problems over k-dimensional simplexes

Abstract

Two classical problems, the Hausdorff moment problem and de Finetti's representation theorem for exchangeable random variables, are considered. We generalize these problems to a g-tuple of k-dimensional simplexes and an infinite sequence of g-fold partially exchangeable random variables in {0,1,...,k}, respectively. The equivalence between them is then formalized and proven.