Typical multifractal box dimensions of measures

摘要

We study the typical behaviour (in the sense of Baire's category) of the multifractal box dimensions of measures on Rd. We prove that in many cases a typical measure it is as irregular as possible, i.e. the lower multifractal box dimensions of μ attain the smallest possible value and the upper multifractal box dimensions of μ attain the largest possible value.