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ArticleOriginal scientific text

Title

Sur les dimensions de mesures

Authors 1

Affiliations

  1. Mathématiques (Bât. I), Université de Cergy-Pontoise, 8, Le Campus 95033 Cergy-Pontoise, France

Abstract

Firstly, we introduce the lower and upper dimensions for a measure defined on a metric space. Secondly, we establish the dimension formulas and characterize the unidimensional measures which were introduced by J.-P. Kahane. Lastly, we give some applications of these to the calculus of dimensions and the multifractal analysis of certain well known measures such as Lebesgue measures on Cantor sets, Gibbs measures, Markov measures and Riesz products etc.

Keywords

ENG
upper and lower dimension, dimension formulas, unidimensional, multifractal, Gibbs measure, Markov measure, Riesz product

Bibliography

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Studia Mathematica
1994/111/1
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Pages:
1-17
Main language of publication
French
Received
1992-07-16
Accepted
1993-02-16
Published
1994
Exact and natural sciences