On The Converse of Rademacher’s Theorem

We will show how to prove a converse to Rademacher’s Theorem, which states that a Lipschitz mapping of $R^n$ to $R^k$ is almost everywhere differentiable. This result (new when $n1$) requires the solution of another problem on structure of sets of zero Lebesgue measure. (Joint work with M. Czornyei.)