Covering $L^p$ spaces by balls
Functional Analysis
2012-12-13 v1 General Topology
Abstract
We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space by closed balls each of positive radius, some point exists in which belongs to infinitely many balls.
Cite
@article{arxiv.1212.2817,
title = {Covering $L^p$ spaces by balls},
author = {Vladimir P. Fonf and Michael Levin and Clemente Zanco},
journal= {arXiv preprint arXiv:1212.2817},
year = {2012}
}