Effective fractal dimensions

  title={Effective fractal dimensions},
  author={Jack H. Lutz},
  journal={Math. Log. Q.},
The two most important notions of fractal dimension are Hausdorff dimension, developed by Hausdorff [17], and packing dimension, developed by Tricot [63] and Sullivan [60]. Both dimensions have the mathematical advantage of being defined from measures, and both have yielded extensive applications in fractal geometry and dynamical systems. In 2000, Lutz [36] proved a simple characterization of Hausdorff dimension in terms of gales, which are betting strategies that generalize martingales… CONTINUE READING


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