Differentiability of Lipschitz Functions in Lebesgue Null Sets

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.

33 pages. Corrected minor misprints and added more detail to the proofs of Lemma 3.2 and Lemma 8.3

References in corpus (3)

• Structure of measures in Lipschitz differentiability spaces
• Differentiability inside sets with upper Minkowski dimension one
• Surfaces Meeting Porous Sets in Positive Measure

Cited by in corpus (1)

• On the differentiability of Lipschitz functions with respect to measures in the Euclidean space