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Differentiability, porosity and doubling in metric measure spaces
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Bate, David and Speight, Gareth (2013) Differentiability, porosity and doubling in metric measure spaces. Proceedings of the American Mathematical Society, 141 (3). pp. 971-985. doi:10.1090/S0002-9939-2012-11457-1 ISSN 0002-9939.
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Official URL: http://dx.doi.org/10.1090/S0002-9939-2012-11457-1
Abstract
We show that if a metric measure space admits a differentiable structure, then porous sets have measure zero and hence the measure is pointwise doubling. We then give a construction to show that if we require only an approximate differentiable structure, the measure need no longer be pointwise doubling.
| 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): | Metric spaces , Function spaces, Nonlinear theories | ||||||||
| Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||||||
| Publisher: | American Mathematical Society | ||||||||
| ISSN: | 0002-9939 | ||||||||
| Official Date: | 2013 | ||||||||
| Dates: |
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| Volume: | 141 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | pp. 971-985 | ||||||||
| DOI: | 10.1090/S0002-9939-2012-11457-1 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | First published in Differentiability, porosity and doubling in metric measure spaces. Proceedings of the American Mathematical Society, 141 (3). pp. 971-985., published by the American Mathematical Society. © Copyright 2012 American Mathematical Society | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 10 February 2020 | ||||||||
| Date of first compliant Open Access: | 21 February 2020 | ||||||||
| RIOXX Funder/Project Grant: |
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