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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 ISSN 1088-6834.
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Official URL: https://doi.org/10.1090/S0894-0347-2014-00810-9
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 | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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| Volume: | 28 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 421-482 | ||||||||
| DOI: | 10.1090/S0894-0347-2014-00810-9 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | 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 | ||||||||
| Date of first compliant deposit: | 25 October 2019 | ||||||||
| Date of first compliant Open Access: | 29 October 2019 | ||||||||
| RIOXX Funder/Project Grant: |
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