# 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} }

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.

## 30 Citations

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- Mathematics
- 2016

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We prove the equivalence of two seemingly very di erent ways of generalising
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