David Bate (Warwick) - "Structure of measures in Lipschitz differentiability spaces"

Abstract

Rademacher's theorem is a classical result asserting the almost everywhere differentiability of Lipschitz functions defined on subsets of Euclidean space. This was recently generalised by Cheeger to certain types of metric measure spaces, where the derivative is defined with respect to a finite collection of Lipschitz functions. This talk will present an alternative notion of differentiation defined by a particular structure of the measure. I will show that these two concepts of differentiability are actually equivalent whenever we have a Rademacher type hypothesis and highlight the properties obtained from this structure of the measure.