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On Approximation of Measures by Their Finite-Dimensional Images

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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.

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Funding

This work was carried out at Lomonosov Moscow State University and supported by the Russian Science Foundation, grant 17-11-01058.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    V. I. Bogachev

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia

    V. I. Bogachev

  3. National Research University Higher School of Economics, Moscow, Russia

    V. I. Bogachev

Authors
  1. V. I. Bogachev
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Correspondence to V. I. Bogachev.

Additional information

Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2021, Vol. 55, pp. 75–81 https://doi.org/10.4213/faa3890.

Translated by V. I. Bogachev

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Bogachev, V.I. On Approximation of Measures by Their Finite-Dimensional Images. Funct Anal Its Appl 55, 236–241 (2021). https://doi.org/10.1134/S0016266321030060

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  • DOI: https://doi.org/10.1134/S0016266321030060

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