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arXiv · 1611.01615

An example of a differentiability space which is PI-unrectifiable

Andrea Schioppa
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Abstract

We construct a (Lipschitz) differentiability space which has at generic points a disconnected tangent and thus does not contain positive measure subsets isometric to positive measure subsets of spaces admitting a Poincar\'e inequality. We also prove that $l^2$-valued Lipschitz maps are differentiable a.e., but there are also Lipschitz maps taking values in some other Banach spaces having the Radon-Nikodym property which fail to be differentiable on sets of positive measure.

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Andrea Schioppa. 2016-11-05. An example of a differentiability space which is PI-unrectifiable. https://arxiv.org/abs/1611.01615

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