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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-2,
author = {Jakub Onufry Wojtaszczyk},
title = {No return to convexity},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {227-239},
zbl = {1213.52008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-2}
}
Jakub Onufry Wojtaszczyk. No return to convexity. Studia Mathematica, Tome 196 (2010) pp. 227-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-3-2/