Geodesic
On approximation of measures by their finite-dimensional images
Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 3, pp. 75-81

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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. 
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     author = {V. I. Bogachev},
     title = {On approximation of measures by their finite-dimensional images},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {75--81},
     publisher = {mathdoc},
     volume = {55},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a5/}
}
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V. I. Bogachev. On approximation of measures by their finite-dimensional images. Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 3, pp. 75-81. http://geodesic.mathdoc.fr/item/FAA_2021_55_3_a5/