No return to convexity
Volume 199 / 2010
Studia Mathematica 199 (2010), 227-239
MSC: Primary 52A23.
DOI: 10.4064/sm199-3-2
Abstract
We study the closures of classes of log-concave measures under taking weak limits, linear transformations and tensor products. We investigate which uniform measures on convex bodies can be obtained starting from some class $\cal K$. In particular we prove that if one starts from one-dimensional log-concave measures, one obtains no non-trivial uniform mesures on convex bodies.
