Differentiability, porosity and doubling in metric measure spaces
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- by David Bate and Gareth Speight PDF
- Proc. Amer. Math. Soc. 141 (2013), 971-985 Request permission
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.References
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Additional Information
- David Bate
- Affiliation: Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL United Kingdom
- Email: D.S.Bate@Warwick.ac.uk
- Gareth Speight
- Affiliation: Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL United Kingdom
- MR Author ID: 1003655
- Email: G.Speight@Warwick.ac.uk
- Received by editor(s): August 1, 2011
- Published electronically: July 27, 2012
- Additional Notes: This work was done under the supervision of David Preiss and was supported by EPSRC
- Communicated by: Mario Bonk
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 971-985
- MSC (2010): Primary 30L99; Secondary 49J52, 53C23
- DOI: https://doi.org/10.1090/S0002-9939-2012-11457-1
- MathSciNet review: 3003689