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arXiv · 1111.2561

A quantitative metric differentiation theorem

Jonas Azzam·Raanan Schul
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Abstract

The purpose of this note is to point out a simple consequence of some earlier work of the authors, "Hard Sard: Quantitative implicit function and extension theorems for Lipschitz maps". For $f$, a Lipschitz function from a Euclidean space into a metric space, we give quantitative estimates for how often the pullback of the metric under $f$ is approximately a seminorm. This is a quantitative version of Kirchheim's metric differentiation result from 1994. Our result is in the form of a Carleson-type estimate.

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Jonas Azzam, Raanan Schul. 2011-11-10. A quantitative metric differentiation theorem. https://arxiv.org/abs/1111.2561

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