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Questions about dimensions of possibly highly irregular or "rough" sets, Hausdorff–Besicovitch dimension and related concepts such as box-counting or Minkowski–Bouligand dimension.
8
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Is there a characterization of the Hausdorff measures?
The spherical Hausdorff measure coincides with the Hausdorff measure on every rectifiable set. However it is possible to find sets where these two measures differ. See Federer 2.10.6
Hence the class …