Csornyei, M and Preiss, D and Tiser, J (2005) Lipschitz functions with unexpectedly large sets of nondifferentiability points. ABSTR APPL ANAL (4) 361 - 373. 10.1155/AAA.2005.361.
Abstract
It is known that every G(delta) subset E of the plane containing a dense set of lines, even if it has measure zero, has the property that every real-valued Lipschitz functions R-2 has a point of differentiability in E. Here we show that the set of points of differentiability of Lipschitz functions inside such sets may be surprisingly tiny: we construct a G(delta) set E subset of R-2 containing a dense set of lines for which there is a pair of real-valued Lipschitz functions on R-2 having no common point of differentiability in E, and there is a real valued Lipschitz function on R-2 whose set of points of differentiability in E is uniformly purely unrectifiable.
| Type: | Article |
|---|---|
| Title: | Lipschitz functions with unexpectedly large sets of nondifferentiability points |
| Open access status: | An open access publication |
| DOI: | 10.1155/AAA.2005.361 |
| Keywords: | FRECHET DIFFERENTIABILITY, BANACH-SPACES |
| UCL classification: | UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics |
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