Typical multifractal box dimensions of measures

Volume 211 / 2011

L. Olsen Fundamenta Mathematicae 211 (2011), 245-266 MSC: Primary 28A80. DOI: 10.4064/fm211-3-3

Abstract

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.

Authors

  • L. OlsenDepartment of Mathematics
    University of St. Andrews
    St. Andrews, Fife KY16 9SS, Scotland
    e-mail

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