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arXiv · 1304.6916

Differentiability of Lipschitz Functions in Lebesgue Null Sets

David Preiss·Gareth Speight
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Abstract

We show that if n>1 then there exists a Lebesgue null set in R^n containing a point of differentiability of each Lipschitz function mapping from R^n to R^(n-1); in combination with the work of others, this completes the investigation of when the classical Rademacher theorem admits a converse. Avoidance of sigma-porous sets, arising as irregular points of Lipschitz functions, plays a key role in the proof.

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David Preiss, Gareth Speight. 2013-04-25. Differentiability of Lipschitz Functions in Lebesgue Null Sets. https://arxiv.org/abs/1304.6916

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