Displaying similar documents to “No return to convexity”

Thin-shell concentration for convex measures

Matthieu Fradelizi, Olivier Guédon, Alain Pajor (2014)

Studia Mathematica

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We prove that for s < 0, s-concave measures on ℝⁿ exhibit thin-shell concentration similar to the log-concave case. This leads to a Berry-Esseen type estimate for most of their one-dimensional marginal distributions. We also establish sharp reverse Hölder inequalities for s-concave measures.

On uniqueness of G-measures and g-measures

Ai Fan (1996)

Studia Mathematica

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We give a simple proof of the sufficiency of a log-lipschitzian condition for the uniqueness of G-measures and g-measures which were studied by G. Brown, A. H. Dooley and M. Keane. In the opposite direction, we show that the lipschitzian condition together with positivity is not sufficient. In the special case where the defining function depends only upon two coordinates, we find a necessary and sufficient condition. The special case of Riesz products is discussed and the Hausdorff dimension...

Narrow Convergence in Spaces of Set-Valued Measures

Kenny Koffi Siggini (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove an analogue of Topsøe's criterion for relative compactness of a family of probability measures which are regular with respect to a family sets. We consider measures whose values are compact convex sets in a locally convex linear topological space.