On barycenters of probability measures

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Abstract
A characterization of the barycenters of Radon probability measures supported on a closed convex subset of a given space is presented. The case of particular interest is studied, in which the underlying space is itself a space of finite signed Radon measures on a metric compact, and the corresponding support is the convex set of probability measures. For locally compact spaces, a simple characterization in terms of the relative interior is found.

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