Seminar Analysis: Giovanni Alberti (University of Pisa)
Rademacher theorem states that every Lipschitz function on the euclidean space is differentiable almost everywhere with respect to the Lebesgue measure. In this talk I will explain how this statement should be modified when the Lebesgue measure is replaced by an arbitrary singular measure, and in particular I will show that the differentiability properties of Lipschitz functions with respect to such a measure are exactly described by the decompositions of the measure in terms of (measures on) rectifiable curves. This result is directly related to recent work by many authors, including myself, David Bate, Marianna Csornyei, Peter Jones, Andrea Marchese, and David Preiss.
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