On relations between entropy and Hausdorff dimension of measures

Athanasios Batakis (1) , Yanick Heurteaux (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Mots clés: Hausdorff dimension; packing dimension; lower and upper dimension; lower and upper entropy

Domaines: Analyse classique [math.CA]

Athanasios Batakis, Yanick Heurteaux. On relations between entropy and Hausdorff dimension of measures. Asian Journal of Mathematics, 2002, 6 (3), pp.399-408. ⟨hal-00475606⟩