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Differentiability of Lipschitz functions in Lebesgue null sets
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Preiss, David and Speight, Gareth (2015) Differentiability of Lipschitz functions in Lebesgue null sets. Inventiones Mathematicae, 199 (2). pp. 517-559. doi:10.1007/s00222-014-0520-5 ISSN 0020-9910.
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Official URL: http://dx.doi.org/10.1007/s00222-014-0520-5
Abstract
We show that if n>1 then there exists a Lebesgue null set in Rn containing a point of differentiability of each Lipschitz function f:Rn→Rn−1; in combination with the work of others, this completes the investigation of when the classical Rademacher theorem admits a converse. Avoidance of σ-porous sets, arising as irregular points of Lipschitz functions, plays a key role in the proof.
| 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, Lebesgue integral, Measure theory | |||||||||
| Journal or Publication Title: | Inventiones Mathematicae | |||||||||
| Publisher: | Springer | |||||||||
| ISSN: | 0020-9910 | |||||||||
| Official Date: | February 2015 | |||||||||
| Dates: |
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| Volume: | 199 | |||||||||
| Number: | 2 | |||||||||
| Page Range: | pp. 517-559 | |||||||||
| DOI: | 10.1007/s00222-014-0520-5 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | This is a post-peer-review, pre-copyedit version of an article published in Inventiones Mathematicae. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00222-014-0520-5 | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 30 October 2019 | |||||||||
| Date of first compliant Open Access: | 30 October 2019 | |||||||||
| RIOXX Funder/Project Grant: |
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