No return to convexity

2009/10/19 by Jakub Onufry Wojtaszczyk, Wojtaszczyk, Jakub Onufry
Mathematics · #52A23 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Probability (math.PR) #math.FA #math.MG #math.PR #msc:52A23

paper · pdf · doi:10.48550/arxiv.0910.3288

14 pages, correction of erroneous statement

arxiv created 2009/10/20 · arxiv updated 2009/12/01

Abstract

In the paper we study closures of classes of log--concave measures under taking weak limits, linear transformations and tensor products. We consider what uniform measures on convex bodies can one obtain starting from some class K. In particular we prove that if one starts from one--dimensional log--concave measures, one obtains no non--trivial uniform mesures on convex bodies.

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