Typical differentiability within an exceptionally small set

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 Csörnyei, Preiss and Tišer, of a universal differentiability set in which a certain Lipschitz function has only a purely unrectifiable set of differentiability points.

arXiv comment33 pages, Appendix 6 pages Accepted for publication in Journal of Mathematical Analysis and Applications. Some revisions made following the referees' feedback