On barycenters of probability measures

Volume 68 / 2020

Sergey Berezin, Azat Miftakhov Bulletin Polish Acad. Sci. Math. 68 (2020), 11-20 MSC: Primary 28C05, 46N30, 60B05, 60B11. DOI: 10.4064/ba191128-31-3 Published online: 20 April 2020


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.


  • Sergey BerezinAix-Marseille Université
    Centrale Marseille, CNRS
    Institut de Mathématiques de Marseille, UMR7373
    39, Rue F. Joliot Curie
    13453 Marseille, France
    St. Petersburg Department of
    V. A. Steklov Mathematical Institute of RAS
    27, Fontanka
    191023 St. Petersburg, Russia
    ORCID: 0000-0003-4885-7794
  • Azat MiftakhovFaculty of Mechanics and Mathematics
    Moscow State University
    1, Leninskiye Gory
    119991 Moscow, Russia

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