# Characterization of n-rectifiability in terms of Jones’ square function: Part II

@article{Azzam2015CharacterizationON,
title={Characterization of n-rectifiability in terms of Jones’ square function: Part II},
author={Jonas Azzam and Xavier Tolsa},
journal={Geometric and Functional Analysis},
year={2015},
volume={25},
pages={1371-1412}
}
• Published 7 January 2015
• Mathematics
• Geometric and Functional Analysis
We show that a Radon measure $${\mu}$$μ in $${\mathbb{R}^d}$$Rd which is absolutely continuous with respect to the n-dimensional Hausdorff measure $${\mathcal{H}^n}$$Hn is n-rectifiable if the so called Jones’ square function is finite $${\mu}$$μ-almost everywhere. The converse of this result is proven in a companion paper by the second author, and hence these two results give a classification of all n-rectifiable measures which are absolutely continuous with respect to $${\mathcal{H}^{n}}$$Hn… Expand
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