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Universal differentiability sets in Laakso space
We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable. This implies that there exists a measure zero universal differentiability set in Laakso space. Additionally, we show that each of the measures constructed supports a Poincare inequality.
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- Award ID(s):
- 2348715
- PAR ID:
- 10589943
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Nonlinear Analysis
- Volume:
- 255
- Issue:
- C
- ISSN:
- 0362-546X
- Page Range / eLocation ID:
- 113752
- Subject(s) / Keyword(s):
- Lipschitz function universal differentiability set Laakso space Poincare inequality
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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