# Quantitative decompositions of Lipschitz mappings into metric spaces

@article{David2020QuantitativeDO, title={Quantitative decompositions of Lipschitz mappings into metric spaces}, author={Guy C. David and Raanan Schul}, journal={arXiv: Metric Geometry}, year={2020} }

We study the quantitative properties of Lipschitz mappings from Euclidean spaces into metric spaces. We prove that it is always possible to decompose the domain of such a mapping into pieces on which the mapping "behaves like a projection mapping" along with a "garbage set" that is arbitrarily small in an appropriate sense. Moreover, our control is quantitative, i.e., independent of both the particular mapping and the metric space it maps into. This improves a theorem of Azzam-Schul from the…

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