The mutual singularity of the relative multifractal measures

Abstract

M. Das proved that the relative multifractal measures are mutually singular for the self-similar measures satisfying the significantly weaker open set condition. The aim of this paper is to show that these measures are mutually singular in a more general framework. As examples, we apply our main results to quasi-Bernoulli measures.

Keywords

• multifractal analysis
• multifractal formalism
• singularity
• 28a78
• 28a80