# Differentiability, porosity and doubling in metric measure spaces

@article{Bate2012DifferentiabilityPA,
title={Differentiability, porosity and doubling in metric measure spaces},
author={David Bate and Gareth Speight},
journal={arXiv: Metric Geometry},
year={2012},
volume={141},
pages={971-985}
}
• Published 1 August 2011
• Mathematics, Economics
• arXiv: Metric Geometry
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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