English

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

R2 v1 2026-06-23T07:07:59.495Z