Inserted: 16 may 2017
Last Updated: 16 may 2017
Journal: Inventiones Mathematicae
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.