Differentiability of Lipschitz Functions in Lebesgue Null Sets
Functional Analysis
2014-03-12 v2 Classical Analysis and ODEs
Abstract
We show that if n>1 then there exists a Lebesgue null set in R^n containing a point of differentiability of each Lipschitz function mapping from R^n to R^(n-1); in combination with the work of others, this completes the investigation of when the classical Rademacher theorem admits a converse. Avoidance of sigma-porous sets, arising as irregular points of Lipschitz functions, plays a key role in the proof.
Cite
@article{arxiv.1304.6916,
title = {Differentiability of Lipschitz Functions in Lebesgue Null Sets},
author = {David Preiss and Gareth Speight},
journal= {arXiv preprint arXiv:1304.6916},
year = {2014}
}
Comments
33 pages. Corrected minor misprints and added more detail to the proofs of Lemma 3.2 and Lemma 8.3