Barycenter in Wasserstein space existence and consistency
Résumé
We study barycenters in the Wasserstein space Pp(E) of a locally compact geodesic space (E, d). In this framework, we define the barycenter of a measure P on Pp(E) as its Fréchet mean. The paper establishes its existence and states consistency with respect to P. We thus extends previous results on R^d , with conditions on P or on the sequence converging to P for consistency.
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