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
DOI:
https://doi.org/10.1090/S0002-9939-2012-11457-1
Published electronically:
July 27, 2012
MathSciNet review:
3003689
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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admitting weak Poincaré inequality, Geometric and Functional Analysis, Volume 10 (2000), Number 1, 111-123. 
porosity and measures, Nonlinearity, Volume 16 (2003), Number 1, 247-255. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 30L99, 49J52, 53C23
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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:
https://doi.org/10.1090/S0002-9939-2012-11457-1
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.
