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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Differentiability, porosity and doubling in metric measure spaces


Authors: David Bate and Gareth Speight
Journal: Proc. Amer. Math. Soc. 141 (2013), 971-985
MSC (2010): Primary 30L99; Secondary 49J52, 53C23
Published electronically: July 27, 2012
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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.


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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
Email: G.Speight@Warwick.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11457-1
PII: S 0002-9939(2012)11457-1
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.