Differentiability of Lipschitz functions in Lebesgue null sets

摘要

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