An analyst’s traveling salesman theorem for sets of dimension larger than one

  title={An analyst’s traveling salesman theorem for sets of dimension larger than one},
  author={Jonas Azzam and Raanan Schul},
  journal={Mathematische Annalen},
In his 1990 Inventiones paper, P. Jones characterized subsets of rectifiable curves in the plane via a multiscale sum of $$\beta $$β-numbers. These $$\beta $$β-numbers are geometric quantities measuring how far a given set deviates from a best fitting line at each scale and location. Jones’ result is a quantitative way of saying that a curve is rectifiable if and only if it has a tangent at almost every point. Moreover, computing this square sum for a curve returns the length of the curve up to… 
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