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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2024, Volume 518, Pages 75–79
DOI: https://doi.org/10.31857/S2686954324040111 (Mi danma553) 		 
MATHEMATICS

Compactification of spaces of measures and pseudocompactness

V. I. Bogachevabcd

a Lomonosov Moscow State University, Moscow, Russia
b National Research University Higher School of Economics, Moscow
c St. Tikhon's Orthodox University, Moscow
d Moscow Center for Fundamental and Applied Mathematics
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DOI: https://doi.org/10.31857/S2686954324040111
Abstract: We prove pseudocompactness of a Tychonoff space $X$ and the space $\mathcal P(X)$ of Radon probability measures on it with the weak topology under the condition that the Stone–Čech compactification of the space $\mathcal P(X)$ is homeomorphic to the space $\mathcal P(\beta X)$ of Radon probability measures on the Stone–Čech compactification of the space $X$.
Keywords: Stone–Čech compactification, space of Radon probability measures, weak topology, pseudocompactness.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics 075-152022-284
The paper is supported by the Ministry of Science and Higher Education of the Russian Federation within the program of the Moscow Center of Fundamental and Applied Mathematics, agreement no. 075-15-2022-284.
Received: 27.03.2024
Revised: 01.08.2024
Accepted: 01.08.2024
English version:
Doklady Mathematics, 2024, Volume 110, Issue 1, Pages 357–360
DOI: https://doi.org/10.1134/S1064562424702181
Bibliographic databases:
Document Type: Article
UDC: 517.518.11, 515.122.252
Language: Russian
Citation: V. I. Bogachev, “Compactification of spaces of measures and pseudocompactness”, Dokl. RAN. Math. Inf. Proc. Upr., 518 (2024), 75–79; Dokl. Math., 110:1 (2024), 357–360
Citation in format AMSBIB
\Bibitem{Bog24}
\by V.~I.~Bogachev
\paper Compactification of spaces of measures and pseudocompactness
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2024
\vol 518
\pages 75--79
\mathnet{http://mi.mathnet.ru/danma553}
\crossref{https://doi.org/10.31857/S2686954324040111}
\elib{https://elibrary.ru/item.asp?id=74176082}
\transl
\jour Dokl. Math.
\yr 2024
\vol 110
\issue 1
\pages 357--360
\crossref{https://doi.org/10.1134/S1064562424702181}
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