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Mat. Sb., 1997, Volume 188, Number 2, Pages 57–66 (Mi msb201)  

This article is cited in 4 scientific papers (total in 4 papers)

On translates of convex measures

E. P. Krugova


Abstract: The following alternative is proved for a convex Radon measure $\mu$, on a locally convex space $X$ and for an arbitrary direction $h\in X$: either $\mu$ is differentiable in the direction $h$ in the sense of Skorokhod and $\|\mu _h-\mu \|\geqslant 2-2e^{-\frac 12\|d_h\mu \|}$, or $\mu$ and $\mu _{th}$ are mutually singular for all $t\in \mathbb R\setminus \{0\}$.

DOI: https://doi.org/10.4213/sm201

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English version:
Sbornik: Mathematics, 1997, 188:2, 227–236

Bibliographic databases:

UDC: 517.987
MSC: 28C15, 28C20
Received: 27.02.1996

Citation: E. P. Krugova, “On translates of convex measures”, Mat. Sb., 188:2 (1997), 57–66; Sb. Math., 188:2 (1997), 227–236

Citation in format AMSBIB
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\by E.~P.~Krugova
\paper On translates of convex measures
\jour Mat. Sb.
\yr 1997
\vol 188
\issue 2
\pages 57--66
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\transl
\jour Sb. Math.
\yr 1997
\vol 188
\issue 2
\pages 227--236
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bobkov, SG, “The size of singular component and shift inequalities”, Annals of Probability, 27:1 (1999), 416  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    2. Kolesnikov, AV, “On diffusion semigroups preserving the log-concavity”, Journal of Functional Analysis, 186:1 (2001), 196  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    3. Kolesnikov, AV, “On semigroups preserving the logarithmic concavity of functions”, Doklady Mathematics, 63:1 (2001), 66  mathscinet  zmath  isi  elib
    4. Kosov E.D., “Fractional Smoothness of Images of Logarithmically Concave Measures Under Polynomials”, J. Math. Anal. Appl., 462:1 (2018), 390–406  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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