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Funktsional'nyi Analiz i ego Prilozheniya, 2021, Volume 55, Issue 3, Pages 75–81
DOI: https://doi.org/10.4213/faa3890 (Mi faa3890) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Brief communications

On approximation of measures by their finite-dimensional images

V. I. Bogachevabc

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Moscow Center for Fundamental and Applied Mathematics
c National Research University "Higher School of Economics", Moscow
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DOI: https://doi.org/10.4213/faa3890
Abstract: We consider Borel measures on separable Banach spaces that are limits of their finite-dimensional images in the weak topology. The class of Banach spaces on which all measures have this property is introduced. The specified property is proved for all measures from the closure in variation of the linear span of the set of measures absolutely continuous with respect to Gaussian measures. Connections with the approximation property and the stochastic approximation property are considered.
Keywords: Borel measure, Gaussian measure, finite-dimensional projection, weak convergence.
Funding agency Grant number
Russian Science Foundation 17-11-01058
Received: 19.02.2021
Revised: 19.02.2021
Accepted: 24.02.2021
English version:
Functional Analysis and Its Applications, 2021, Volume 55, Issue 3, Pages 236–241
DOI: https://doi.org/10.1134/S0016266321030060
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: V. I. Bogachev, “On approximation of measures by their finite-dimensional images”, Funktsional. Anal. i Prilozhen., 55:3 (2021), 75–81; Funct. Anal. Appl., 55:3 (2021), 236–241
Citation in format AMSBIB
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    • 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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