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. 

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