Remarque sur un théorème de M. Hurewicz
Samuel Eilenberg (1935)
Fundamenta Mathematicae
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Samuel Eilenberg (1935)
Fundamenta Mathematicae
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Micheline Vigué-Poirrier (1984)
Annales scientifiques de l'École Normale Supérieure
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Casimir Kuratowski (1935)
Fundamenta Mathematicae
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Karol Borsuk (1937)
Fundamenta Mathematicae
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Casimir Kuratowski (1937)
Fundamenta Mathematicae
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Jean Leray (1959)
Bulletin de la Société Mathématique de France
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W. Nitka (1961)
Colloquium Mathematicae
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Samuel Eilenberg (1935)
Fundamenta Mathematicae
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Ai Fan (1994)
Studia Mathematica
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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.