# Differentiability of Lipschitz functions w.r.t. Radon measures.

### (MPI MIS Leipzig (to date))

**Event:** ERC Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis

**Date:** Oct 08, 2013,
**time:** 16:40

**Abstract.** In this talk I will show an adapted version of Rademacher theorem (Lipschitz functions are Lebesgue a.e. differentiable) when the Lebesgue measure is replaced by a generical Radon measure. I will explain how to associate to any Radon measure \(\mu\) a bundle of vector spaces such that every Lipschitz function is \(\mu\)-almost everywhereÂ differentiable along the vector space given by the bundle. I will also show that this bundle is optimal, exhibiting a Lipschitz function which is \(\mu\)-a.e. non differentiable along any direction which does not lie in the bundle. This is joint work with Giovanni Alberti.