No return to convexity

Details No return to convexity No return to convexity

2009-10-19

arxiv.org/abs/0910.3288v2

Mathematics

Functional Analysis

14 pages, correction of erroneous statement

Scientific paper

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 $\mathcal{K}$. 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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