Year: 2014
Type: article
Abstract: We prove the equivalence of two seemingly very different ways of generalising Rademacher’s theorem to metric measure spaces. One such generalisation is based upon the notion of forming partial derivatives along a very rich structure of Lipschitz curves in a way analogous to the differentiability theory of Euclidean spaces. This approach to differentiability in this generality appears here for the first time and by examining this structure further, we naturally arrive to several descriptions of Lipschitz differentiability spaces.
Author: David Bate
Institutions: University of Warwick, University of Chicago
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1973507952