# Characterising rectifiable metric spaces using tangent spaces

@inproceedings{Bate2021CharacterisingRM, title={Characterising rectifiable metric spaces using tangent spaces}, author={David Bate}, year={2021} }

We characterise rectifiable subsets of a complete metric space X in terms of local approximation, with respect to the Gromov–Hausdorff distance, by an n-dimensional Banach space. In fact, if E ⊂ X with Hn(E) < ∞ and has positive lower density almost everywhere, we prove that it is sufficient that, at almost every point and each sufficiently small scale, E is approximated by a bi-Lipschitz image of Euclidean space. We also introduce a generalisation of Preiss’s tangent measures that is suitable…

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