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On the differentiability of Lipschitz functions with respect to measures in the Euclidean space
Giovanni Alberti and Andrea MarcheseAbstract
Rademacher theorem states that every Lipschitz function on the Euclidean space is differentiable almost everywhere, where "almost everywhere" refers to the Lebesgue measure. Our main result is an extension of this theorem where the Lebesgue measure is replaced by an arbitrary measure
In particular we show that the differentiability properties of Lipschitz functions at
In the process we obtain a differentiability result for Lipschitz functions with respect to (measures associated to)
- Received:
- 11.08.14
- Published:
- 15.08.14
- MSC Codes:
- 26B05, 49Q15, 26A27, 28A75, 46E35
- Keywords:
- Lipschitz functions, differentiability, Rademacher theorem, normal currents