Multifractal spectra of typical and prevalent measures

TL;DR

This paper explores the typical multifractal spectra of measures supported on compact sets, revealing that most such measures have a linear lower singularity spectrum in the Baire category sense.

Contribution

It demonstrates that, generically, measures supported on compact sets exhibit a linear lower singularity spectrum, advancing understanding of multifractal properties in a Baire category framework.

Findings

Typical measures have a linear lower singularity spectrum

Results are obtained in the Baire category sense

Analysis extends to upper singularity spectrum and other genericity forms

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.