Calculus of Variations and Geometric Measure Theory

D. Bate - G. Speight

Differentiability, Porosity and Doubling in Metric Measure Spaces

created by speight on 16 May 2017


Published Paper

Inserted: 16 may 2017
Last Updated: 16 may 2017

Journal: Proceedings of the American Mathematical Society
Volume: 141 (2013)
Pages: 971-985
Year: 2011

ArXiv: 1108.0318 PDF


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.