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Funktsional'nyi Analiz i ego Prilozheniya, 2024, Volume 58, Issue 1, Pages 4–21
DOI: https://doi.org/10.4213/faa4184
(Mi faa4184)
 

This article is cited in 2 scientific papers (total in 2 papers)

On compactification of spaces of measures

Vladimir Bogachevab

a Lomonosov Moscow State University
b HSE University, Moscow
References:
Abstract: In this paper, we compare the Stone–Čech compactification $\beta \mathcal{P}(X)$ of the space $\mathcal{P}(X)$ of Radon probability measures on a Tychonoff space $X$, equipped with the weak topology, with the space $\mathcal{P}(\beta X)$ of Radon probability measures on the Stone–Čech compactification $\beta X$ of the space $X$. It is shown that for any noncompact metric space $X$, the compactification $\beta \mathcal{P}(X)$ does not coincide with $\mathcal{P}(\beta X)$. We discuss the case of more general Tychonoff spaces and also the case of the Samuel compactification, for which the coincidence holds.
Keywords: Radon measure, weak topology, Stone–Čech compactification, Samuel compactification, compactification of the space of measures.
Funding agency Grant number
Russian Science Foundation 22-11-00015
This research is supported by the Russian Science Foundation grant no. 22-11-00015 (at Lomonosov Moscow State University), https://rscf.ru/en/project/22-11-00015/.
Received: 01.12.2023
Revised: 01.12.2023
Accepted: 04.12.2023
English version:
Functional Analysis and Its Applications, 2024, Volume 58, Issue 1, Pages 2–15
DOI: https://doi.org/10.1134/S0016266324010027
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Vladimir Bogachev, “On compactification of spaces of measures”, Funktsional. Anal. i Prilozhen., 58:1 (2024), 4–21; Funct. Anal. Appl., 58:1 (2024), 2–15
Citation in format AMSBIB
\Bibitem{Bog24}
\by Vladimir Bogachev
\paper On compactification of spaces of measures
\jour Funktsional. Anal. i Prilozhen.
\yr 2024
\vol 58
\issue 1
\pages 4--21
\mathnet{http://mi.mathnet.ru/faa4184}
\crossref{https://doi.org/10.4213/faa4184}
\transl
\jour Funct. Anal. Appl.
\yr 2024
\vol 58
\issue 1
\pages 2--15
\crossref{https://doi.org/10.1134/S0016266324010027}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85189784574}
Linking options:
  • https://www.mathnet.ru/eng/faa4184
  • https://doi.org/10.4213/faa4184
  • https://www.mathnet.ru/eng/faa/v58/i1/p4
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Full-text PDF :11
    Russian version HTML:29
    References:46
    First page:38
     
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