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Bulletin of Irkutsk State University. Series Mathematics, 2023, Volume 44, Pages 19–30
DOI: https://doi.org/10.26516/1997-7670.2023.44.19 (Mi iigum522) 		 
This article is cited in 1 scientific paper (total 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
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DOI: https://doi.org/10.26516/1997-7670.2023.44.19
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.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-284
This research is supported by the Saint Tikhon’s Orthodox University and the Foundation “Living tradition” (the results in Section 2) and by the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement No. 075-15-2022-284 (the results in Section 3).
Received: 08.11.2022
Revised: 16.01.2023
Accepted: 23.01.2023
Document Type: Article
UDC: 517.9
MSC: 28C15, 28A33, 46E27
Language: English
Citation: Vladimir I. Bogachev, Svetlana N. Popova, “On Radon barycenters of measures on spaces of measures”, Bulletin of Irkutsk State University. Series Mathematics, 44 (2023), 19–30
Citation in format AMSBIB
\Bibitem{BogPop23}
\by Vladimir~I.~Bogachev, Svetlana~N.~Popova
\paper On Radon barycenters of measures on spaces of measures
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2023
\vol 44
\pages 19--30
\mathnet{http://mi.mathnet.ru/iigum522}
\crossref{https://doi.org/10.26516/1997-7670.2023.44.19}
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