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Sbornik: Mathematics, 2005, Volume 196, Issue 3, Pages 309–335
DOI: https://doi.org/10.1070/SM2005v196n03ABEH000882
(Mi sm1271)
 

This article is cited in 83 scientific papers (total in 84 papers)

Triangular transformations of measures

V. I. Bogachev, A. V. Kolesnikov, K. V. Medvedev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: A new identity for the entropy of a non-linear image of a measure on $\mathbb R^n$ is obtained, which yields the well-known Talagrand's inequality. Triangular mappings on $\mathbb R^n$ and $\mathbb R^\infty$ are studied, that is, mappings $T$ such that the $i$th coordinate function $T_i$ depends only on the variables $x_1,\dots,x_i$. With the help of such mappings the well-known open problem on the representability of each probability measure that is absolutely continuous with respect to a Gaussian measure $\gamma$ on an infinite dimensional space as the image of $\gamma$ under a map of the form $T(x)=x+F(x)$ where $F$ takes values in the Cameron–Martin space of the measure $\gamma$ is solved in the affirmative. As an application, a generalized logarithmic Sobolev inequality is also proved.
Received: 27.05.2004
Bibliographic databases:
UDC: 519.2
MSC: 28C20, 46G12, 60B11
Language: English
Original paper language: Russian
Citation: V. I. Bogachev, A. V. Kolesnikov, K. V. Medvedev, “Triangular transformations of measures”, Sb. Math., 196:3 (2005), 309–335
Citation in format AMSBIB
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\paper Triangular transformations of measures
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\yr 2005
\vol 196
\issue 3
\pages 309--335
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Linking options:
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    Citing articles in Google Scholar: Russian citations, English citations
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    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:1144
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    References:87
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