Differentiability, Porosity and Doubling in Metric Measure Spaces
Abstract
We show 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 if we only require an approximate differentiable structure the measure need no longer be pointwise doubling.
 Publication:

arXiv eprints
 Pub Date:
 August 2011
 DOI:
 10.48550/arXiv.1108.0318
 arXiv:
 arXiv:1108.0318
 Bibcode:
 2011arXiv1108.0318B
 Keywords:

 Mathematics  Metric Geometry;
 30L99;
 49J52;
 53C23
 EPrint:
 Proc. Amer. Math. Soc. 141 (2013), pp. 971985