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On barycenters of probability measures

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arxiv 1911.07680 v2 pith:SEQ4XXTN submitted 2019-11-18 math.PR math.FA

Sergey Berezin , Azat Miftakhov This is my paper · ORCID
classification math.PRmath.FA
keywords measuresprobabilityspacebarycenterscharacterizationcompactconvexradon
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A characterization is presented of barycenters of the Radon probability measures supported on a closed convex subset of a given space. A case of particular interest is studied, where the underlying space is itself the space of finite signed Radon measures on a metric compact and where the corresponding support is the convex set of probability measures. For locally compact spaces, a simple characterization is obtained in terms of the relative interior.

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