Csornyei, M; Preiss, D; Tiser, J; (2005) Lipschitz functions with unexpectedly large sets of nondifferentiability points. ABSTR APPL ANAL (4) 361 - 373. 10.1155/AAA.2005.361.
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.
|Title:||Lipschitz functions with unexpectedly large sets of nondifferentiability points|
|Open access status:||An open access publication|
|Keywords:||FRECHET DIFFERENTIABILITY, BANACH-SPACES|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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