Multifractal spectra of typical and prevalent measures

Abstract

We prove that, in the Baire category sense, a typical measure supported by a compact set admits a linear lower singularity spectrum. We investigate the same question for the upper singularity spectrum and for other forms of genericity.

References in corpus (3)

• Typical Borel measures on $[0,1]d$ satisfy a multifractal formalism
• How behave the typical $L^q$-dimensions of measures?
• Multifractal analysis of the divergence of Fourier series: the extreme cases

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