Geodesic
Typical multifractal box dimensions of measures
L. Olsen1
1 Department of Mathematics University of St. Andrews St. Andrews, Fife KY16 9SS, Scotland
Fundamenta Mathematicae, Tome 211 (2011) no. 3, pp. 245-266

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study the typical behaviour (in the sense of Baire's category) of the multifractal box dimensions of measures on $\mathbb R^{d}$. We prove that in many cases a typical measure $\mu$ is as irregular as possible, i.e. the lower multifractal box dimensions of $\mu$ attain the smallest possible value and the upper multifractal box dimensions of $\mu$ attain the largest possible value.
DOI : 10.4064/fm211-3-3
Keywords: study typical behaviour sense baires category multifractal box dimensions measures mathbb prove many cases typical measure irregular possible lower multifractal box dimensions attain smallest possible value upper multifractal box dimensions attain largest possible value

L. Olsen 1

1 Department of Mathematics University of St. Andrews St. Andrews, Fife KY16 9SS, Scotland 
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L. Olsen. Typical multifractal box dimensions of measures. Fundamenta Mathematicae, Tome 211 (2011) no. 3, pp. 245-266. doi: 10.4064/fm211-3-3

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