A universal differentiability set in Banach spaces with separable dual
Functional Analysis
2011-03-29 v1
Abstract
We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Fr\'echet differentiable somewhere in S.
Cite
@article{arxiv.1103.5094,
title = {A universal differentiability set in Banach spaces with separable dual},
author = {Michael Doré and Olga Maleva},
journal= {arXiv preprint arXiv:1103.5094},
year = {2011}
}
Comments
41 pages, 1 figure