Calculus of Variations and Geometric Measure Theory
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D. Preiss - G. Speight

Differentiability of Lipschitz Functions in Lebesgue Null Sets

created by speight on 16 May 2017

[BibTeX]

Published Paper

Inserted: 16 may 2017
Last Updated: 16 may 2017

Journal: Inventiones Mathematicae
Volume: 199
Number: 2
Pages: 517-559
Year: 2013

ArXiv: 1304.6916 PDF

Abstract:

We show that if n>1 then there exists a Lebesgue null set in Rn containing a point of differentiability of each Lipschitz function mapping from Rn 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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