Typical multifractal box dimensions of measures
Volume 211 / 2011
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.
