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.
@article{bwmeta1.element.bwnjournal-article-smv111i1p1bwm,
author = {Ai Fan},
title = {Sur les dimensions de mesures},
journal = {Studia Mathematica},
volume = {108},
year = {1994},
pages = {1-17},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv111i1p1bwm}
}
Fan, Ai. Sur les dimensions de mesures. Studia Mathematica, Tome 108 (1994) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv111i1p1bwm/
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