# A quantitative metric differentiation theorem

@article{Azzam2011AQM,
title={A quantitative metric differentiation theorem},
author={Jonas Azzam and Raanan Schul},
journal={arXiv: Metric Geometry},
year={2011}
}
• Published 2011
• Mathematics
• arXiv: Metric Geometry
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… Expand
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