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Structure of measures in Lipschitz differentiability spaces

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Bate, David (2015) Structure of measures in Lipschitz differentiability spaces. Journal of the American Mathematical Society, 28 (2). pp. 421-482. doi:10.1090/S0894-0347-2014-00810-9

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Official URL: https://doi.org/10.1090/S0894-0347-2014-00810-9

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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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Lipschitz spaces , Euclidean algorithm, Function spaces
Journal or Publication Title: Journal of the American Mathematical Society
Publisher: American Mathematical Society
ISSN: 1088-6834
Official Date: 2015
Dates:
DateEvent
2015Published
4 June 2014Available
6 February 2014Accepted
Volume: 28
Number: 2
Page Range: pp. 421-482
DOI: 10.1090/S0894-0347-2014-00810-9
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: First published in Journal of the American Mathematical Society in 28 (2) 2014, published by the American Mathematical Society. © Copyright 2014 American Mathematical Society
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
UNSPECIFIED[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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