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Dimension of measures: the probabilistic approach

Yanick Heurteaux

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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.

Article information

Publ. Mat., Volume 51, Number 2 (2007), 243-290.

First available in Project Euclid: 31 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28A12: Contents, measures, outer measures, capacities 28A78: Hausdorff and packing measures 60F10: Large deviations
Secondary: 28D05: Measure-preserving transformations 28D20: Entropy and other invariants 60F20: Zero-one laws

Hausdorff dimension packing dimension lower and upper dimension of a measure multifractal analysis quasi-Bernoulli measures


Heurteaux, Yanick. Dimension of measures: the probabilistic approach. Publ. Mat. 51 (2007), no. 2, 243--290.

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