A compact null set containing a differentiability point of every Lipschitz function

Details A compact null set containing a differentiability point of every Lipschitz function A compact null set containing a differentiability point of every Lipschitz function

2008-04-29

arxiv.org/abs/0804.4576v3

Mathematische Annalen, Online First, 26 November 2010

Mathematics

Functional Analysis

28 pages; minor modifications throughout; Lemma 4.2 is proved for general Banach space rather than for Hilbert space

Scientific paper

10.1007/s00208-010-0613-4

We prove that in a Euclidean space of dimension at least two, there exists a
compact set of Lebesgue measure zero such that any real-valued Lipschitz
function defined on the space is differentiable at some point in the set. Such
a set is constructed explicitly.

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