On barycenters of probability measures

Sergey Berezin, Azat Miftakhov
2020 Bulletin of the Polish Academy of Sciences Mathematics  
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. 2020 Mathematics Subject Classification:
more » ... Classification: Primary 28C05, 46N30, 60B05, 60B11.
doi:10.4064/ba191128-31-3 fatcat:nfv7vlpeujc2dhmramxin45ree