No return to convexity

Jakub Onufry Wojtaszczyk. "No return to convexity." Studia Mathematica 199.3 (2010): 227-239. <http://eudml.org/doc/286688>.

@article{JakubOnufryWojtaszczyk2010,
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 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.},
author = {Jakub Onufry Wojtaszczyk},
journal = {Studia Mathematica},
keywords = {log-concave measure; product measure; weak limit; linear map; closure},
language = {eng},
number = {3},
pages = {227-239},
title = {No return to convexity},
url = {http://eudml.org/doc/286688},
volume = {199},
year = {2010},
}

TY - JOUR
AU - Jakub Onufry Wojtaszczyk
TI - No return to convexity
JO - Studia Mathematica
PY - 2010
VL - 199
IS - 3
SP - 227
EP - 239
AB - 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.
LA - eng
KW - log-concave measure; product measure; weak limit; linear map; closure
UR - http://eudml.org/doc/286688
ER -