A compact null set containing a differentiability point of every Lipschitz function
Functional Analysis
2011-05-17 v3 Classical Analysis and ODEs
Abstract
We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly.
Cite
@article{arxiv.0804.4576,
title = {A compact null set containing a differentiability point of every Lipschitz function},
author = {Michael Doré and Olga Maleva},
journal= {arXiv preprint arXiv:0804.4576},
year = {2011}
}
Comments
28 pages; minor modifications throughout; Lemma 4.2 is proved for general Banach space rather than for Hilbert space