Athanasios Batakis, Yanick Heurteaux
Abstract
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We characterize probability measures whose Hausdorff dimension or packing dimension can be calculated by an entropy formula.In particular, we prove that such measures are unidimensional.We also construct examples of unidimensional measures for which entropy does not calculate the dimension.
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We characterize probability measures whose Hausdorff dimension or packing dimension can be calculated by an entropy formula.In particular, we prove that such measures are unidimensional.We also construct examples of unidimensional measures for which entropy does not calculate the dimension.
Key concepts: Mathematics, Hausdorff dimension, Minkowski–Bouligand dimension, Effective dimension, Hausdorff space, Entropy (arrow of time), Packing dimension, Hausdorff measure