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JOURNALS // Bulletin of Irkutsk State University. Series Mathematics // Archive

Bulletin of Irkutsk State University. Series Mathematics, 2023 Volume 44, Pages 19–30 (Mi iigum522)

This article is cited in 1 paper

Integro-differential equations and functional analysis

On Radon barycenters of measures on spaces of measures

Vladimir I. Bogachevabcd, Svetlana N. Popovabe

a Lomonosov Moscow State University, Moscow, Russian Federation
b National Research University Higher School of Economics, Moscow, Russian Federation
c Saint Tikhon's Orthodox University, Moscow, Russian Federation
d Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation
e Moscow Institute of Physics and Technology (State University), Dolgoprudny, Russian Federation

Abstract: We study metrizability of compact sets in spaces of Radon measures with the weak topology. It is shown that if all compacta in a given completely regular topological space are metrizable, then every uniformly tight compact set in the space of Radon measures on this space is also metrizable. It is proved that the property that compact sets of measures on a given space are metrizable is preserved for products of this space with spaces that can be embedded into separable metric spaces. In addition, we construct a Radon probability measure on the space of Radon probability measures on a completely regular space such that its barycenter is not a Radon measure.

Keywords: Radon measure, barycenter, metrizable compact set of measures.

UDC: 517.9

MSC: 28C15, 28A33, 46E27

Received: 08.11.2022
Revised: 16.01.2023
Accepted: 23.01.2023

Language: English

DOI: 10.26516/1997-7670.2023.44.19



© Steklov Math. Inst. of RAS, 2024