Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590910 | Journal of Functional Analysis | 2013 | 17 Pages |
Abstract
We formulate and study an optimal transportation problem with infinitely many marginals; this is a natural extension of the multi-marginal problem studied by Gangbo and Świȩch (1998) [15], . We prove results on the existence, uniqueness and characterization of the optimizer, which are natural extensions of the results in Gangbo and Świȩch (1998) [15], . The proof relies on a relationship between this problem and the problem of finding barycenters in the Wasserstein space, a connection first observed for finitely many marginals by Agueh and Carlier (2011) [1].
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