Doubling subsets of Hilbert space admit pointwise and coarse tangent fields whose dimension is bounded by the Nagata or Assouad dimension of the set.
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Introduces a measure-dependent relaxation of bounded-length-distortion and establishes existence of such maps from finite-Hausdorff-dimension metric measure spaces into finite-dimensional normed spaces.
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Coarse and pointwise tangent fields
Doubling subsets of Hilbert space admit pointwise and coarse tangent fields whose dimension is bounded by the Nagata or Assouad dimension of the set.