Differentiability, porosity and doubling in metric measure spaces

Bate, David; Speight, Gareth

doi:10.1090/S0002-9939-2012-11457-1

Differentiability, porosity and doubling in metric measure spaces
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by David Bate and Gareth Speight PDF

Proc. Amer. Math. Soc. 141 (2013), 971-985 Request permission

Abstract:

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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