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 e-prints
- Pub Date:
- August 2011
- DOI:
- 10.48550/arXiv.1108.0318
- arXiv:
- arXiv:1108.0318
- Bibcode:
- 2011arXiv1108.0318B
- Keywords:
-
- Mathematics - Metric Geometry;
- 30L99;
- 49J52;
- 53C23
- E-Print:
- Proc. Amer. Math. Soc. 141 (2013), pp. 971-985