On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets
Studia Mathematica, Tome 105 (1993) no. 2, pp. 173-187
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
The paper deals with the following conjecture: if μ is a centered Gaussian measure on a Banach space F,λ > 1, K ⊂ F is a convex, symmetric, closed set, P ⊂ F is a symmetric strip, i.e. P = {x ∈ F : |x'(x)| ≤ 1} for some x' ∈ F', such that μ(K) = μ(P) then μ(λK) ≥ μ(λP). We prove that the conjecture is true under the additional assumption that K is "sufficiently symmetric" with respect to μ, in particular it is true when K is a ball in Hilbert space. As an application we give estimates of Gaussian measures of large and small balls in a Hilbert space.
@article{10_4064_sm_105_2_173_187,
author = {Stanis{\l}aw Kwapie\'n},
title = {On some conjecture concerning {Gaussian} measures of dilatations of convex symmetric sets},
journal = {Studia Mathematica},
pages = {173--187},
publisher = {mathdoc},
volume = {105},
number = {2},
year = {1993},
doi = {10.4064/sm-105-2-173-187},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-105-2-173-187/}
}
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Stanisław Kwapień. On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets. Studia Mathematica, Tome 105 (1993) no. 2, pp. 173-187. doi: 10.4064/sm-105-2-173-187
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