Structure of measures in Lipschitz differentiability spaces

Bate, David^1, 2

¹Department of Mathematics, Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, UK
²Department of Mathematics, University of Chicago, 5734 S. University Avenue, Room 208C, Chicago, Illinois 60637

Journal of the American Mathematical Society, Tome 28 (2015) no. 2, pp. 421-482

Résumé

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.

Détail

DOI : 10.1090/S0894-0347-2014-00810-9

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