Necessary Condition for Rectifiability Involving Wasserstein Distance W2

@inproceedings{Dkabrowski2020NecessaryCF,
  title={Necessary Condition for Rectifiability Involving Wasserstein Distance W2},
  author={Damian Dkabrowski},
  year={2020}
}
A Radon measure μ is n-rectifiable if μ ≪ H n and μ-almost all of supp μ can be covered by Lipschitz images of R. In this paper we give a necessary condition for rectifiability in terms of the so-called α2 numbers – coefficients quantifying flatness using Wasserstein distance W2. In a recent article we showed that the same condition is also sufficient for rectifiability, and so we get a new characterization of rectifiable measures. 
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