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{bwmeta1.element.bwnjournal-article-smv105i2p173bwm,
author = {Stanis\l aw Kwapie\'n and Jerzy Sawa},
title = {On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {173-187},
zbl = {0810.60035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv105i2p173bwm}
}
Kwapień, Stanisław; Sawa, Jerzy. On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets. Studia Mathematica, Tome 104 (1993) pp. 173-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv105i2p173bwm/
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