Dimension of measures : the probabilistic approach

Yanick Heurteaux (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

Various tools can be used to calculate or estimate the dimension of measures. Using a probabilistic interpretation, we propose very simple proofs for the main inequalities related to this notion. We also discuss the case of quasi-Bernoulli measures and point out the deep link existing between the calculation of the dimension of auxiliary measures and the multifractal analysis.

Mots clés: Hausdorff dimension; packing dimension; lower and upper dimension of a measure; multifractal analysis; quasi-Bernoulli measures

Domaines: Analyse classique [math.CA]; Probabilités [math.PR]

Yanick Heurteaux. Dimension of measures : the probabilistic approach. Publicacions Matemàtiques, 2007, 51, pp.243-290. ⟨hal-00475246⟩