Fubini-Tonelli type theorem for non product measures in a product space
Probability
2018-06-12 v1
Abstract
I prove a theorem about iterated integrals for non-product measures in a product space. The first task is to show the existence of a family of measures on the second space, indexed by the points on of the first space (outside a negligible set), such that integrating the measures on the index against the first marginal gives back the original measure (see Theorem 2.1). At the end, I give a simple application in Optimal Transport.
Keywords
Cite
@article{arxiv.1806.04124,
title = {Fubini-Tonelli type theorem for non product measures in a product space},
author = {Jorge Salazar},
journal= {arXiv preprint arXiv:1806.04124},
year = {2018}
}