On the structure of universal differentiability sets
Functional Analysis
2016-07-21 v1
Abstract
We prove that universal differentiability sets in Euclidean spaces possess distinctive structural properties. Namely, we show that any universal differentiability set contains a `kernel' in which the points of differentiability of each Lipschitz function are dense. We further prove that no universal differentiability set may be decomposed as a countable union of relatively closed, non-universal differentiability sets. The sharpness of this result, with respect to existing decomposibility results of the opposite nature, is discussed.
Cite
@article{arxiv.1607.05933,
title = {On the structure of universal differentiability sets},
author = {Michael Dymond},
journal= {arXiv preprint arXiv:1607.05933},
year = {2016}
}