Typical differentiability within an exceptionally small set
Functional Analysis
2020-06-19 v2 Classical Analysis and ODEs
Abstract
We verify the existence of a purely unrectifiable set in which the typical Lipschitz function has a large set of full differentiability points. The example arises from a construction, due to Cs\"ornyei, Preiss and Ti\v{s}er, of a universal differentiability set in which a certain Lipschitz function has only a purely unrectifiable set of differentiability points.
Keywords
Cite
@article{arxiv.1901.03133,
title = {Typical differentiability within an exceptionally small set},
author = {Michael Dymond},
journal= {arXiv preprint arXiv:1901.03133},
year = {2020}
}
Comments
33 pages, Appendix 6 pages Accepted for publication in Journal of Mathematical Analysis and Applications. Some revisions made following the referees' feedback