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Keywords:
metric dimension; limit capacity; entropy dimension; box-counting dimension; Hausdorff dimension; Kolmogorov dimension; Minkowski dimension; Bouligand dimension; converging sequences; convex sequences; differentiable function
metric dimension; limit capacity; entropy dimension; box-counting dimension; Hausdorff dimension; Kolmogorov dimension; Minkowski dimension; Bouligand dimension; converging sequences; convex sequences; differentiable function
Summary:
Converging sequences in metric space have Hausdorff dimension zero, but their metric dimension (limit capacity, entropy dimension, box-counting dimension, Hausdorff dimension, Kolmogorov dimension, Minkowski dimension, Bouligand dimension, respectively) can be positive. Dimensions of such sequences are calculated using a different approach for each type. In this paper, a rather simple formula for (lower, upper) metric dimension of any sequence given by a differentiable convex function, is derived.
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