Geodesic
On barycenters of probability measures
Sergey Berezin 1   ; Azat Miftakhov 2
1 Aix-Marseille Université Centrale Marseille, CNRS Institut de Mathématiques de Marseille, UMR7373 39, Rue F. Joliot Curie 13453 Marseille, France and St. Petersburg Department of V. A. Steklov Mathematical Institute of RAS 27, Fontanka 191023 St. Petersburg, Russia <a href="https://orcid.org/0000-0003-4885-7794">ORCID: 0000-0003-4885-7794</a>
2 Faculty of Mechanics and Mathematics Moscow State University 1, Leninskiye Gory 119991 Moscow, Russia
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 68 (2020) no. 1, pp. 11-20 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba191128-31-3
Keywords: characterization presented barycenters radon probability measures supported closed convex subset given space particular interest studied where underlying space itself space finite signed radon measures metric compact where corresponding support convex set probability measures locally compact spaces simple characterization obtained terms relative interior

Sergey Berezin  1   ; Azat Miftakhov  2

1 Aix-Marseille Université Centrale Marseille, CNRS Institut de Mathématiques de Marseille, UMR7373 39, Rue F. Joliot Curie 13453 Marseille, France and St. Petersburg Department of V. A. Steklov Mathematical Institute of RAS 27, Fontanka 191023 St. Petersburg, Russia <a href="https://orcid.org/0000-0003-4885-7794">ORCID: 0000-0003-4885-7794</a>
2 Faculty of Mechanics and Mathematics Moscow State University 1, Leninskiye Gory 119991 Moscow, Russia 
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     title = {On barycenters of probability measures},
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Sergey Berezin; Azat Miftakhov. On barycenters of probability measures. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 68 (2020) no. 1, pp. 11-20. doi: 10.4064/ba191128-31-3

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