Fubini-Tonelli type theorem for non product measures in a product space

Jorge Salazar

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arXiv · 1806.04124

Fubini-Tonelli type theorem for non product measures in a product space

Jorge Salazar

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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.

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Jorge Salazar. 2018-06-11. Fubini-Tonelli type theorem for non product measures in a product space. https://arxiv.org/abs/1806.04124

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