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We show that if n>1 then there exists a Lebesgue null set in R^n containing apoint of differentiability of each Lipschitz function mapping from R^n toR^(n-1); in combination with the work of others, this completes theinvestigation of when the classical Rademacher theorem admits a converse.Avoidance of sigma-porous sets, arising as irregular points of Lipschitzfunctions, plays a key role in the proof.

Differentiability of Lipschitz Functions in Lebesgue Null Sets