# 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} }

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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