Abstract: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. \par In this paper, a rather simple formula for (lower, upper) metric dimension of any sequence given by a differentiable convex function, is derived.
Keywords: metric dimension, limit capacity, entropy dimension, box-counting dimension, Hausdorff dimension, Kolmogorov dimension, Minkowski dimension, Bouligand dimension, converging sequences, convex sequences, differentiable function
AMS Subject Classification: 54F50, 40A05