Differentiability of Lipschitz Functions in Lebesgue Null Sets (1304.6916v2)

Published 25 Apr 2013 in math.FA and math.CA

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.

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Generate a whiteboard explanation of this paper.

Sign Up to Generate

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Top Community Prompts

Explain it Like I'm 14

Practical Applications

Conceptual Simplification

Sign Up to Activate View All Prompts

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (2)

Collections

Sign up for free to add this paper to one or more collections.