# Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space

@article{Schul2007BiLipschitzDO,
title={Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space},
author={Raanan Schul},
journal={Revista Matematica Iberoamericana},
year={2007},
volume={25},
pages={521-531}
}
• R. Schul
• Published 22 February 2007
• Mathematics
• Revista Matematica Iberoamericana
We prove a quantitative version of the following statement. Given a Lipschitz function f from the k-dimensional unit cube into a general metric space, one can decomposed f into a finite number of BiLipschitz functions f|_{F_i} so that the k-Hausdorff content of f([0,1]^k\setminus \cup F_i) is small. We thus generalize a theorem of P. Jones (1988) from the setting of R^d to the setting of a general metric space. This positively answers problem 11.13 in Fractured Fractals and Broken Dreams" by…
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