On barycenters of probability measures
Volume 68 / 2020
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.