Some density results of relative multifractal analysis

The mutual singularity of the relative multifractal measures

“…This formalism is based on the ideas of the "multifractal formalism" as clari ed by Olsen [15]. Later, in [1,3,10,21], Selmi et al justi ed the relative multifractal formalism under less restrictive hypotheses. Other studies have been developed in the same direction such as [2,9,19,20,22,24].…”

Relative multifractal box-dimensions

“…Later, Ben Nasr et al in [11,12] developed a necessary and sufficient condition for the validity of the multifractal formalism. As an application, we can refer to the multifractal structure of one graph directed self-conformal measure with respect to another (see for example [3,17,21]).…”

On the Projections of the Mutual Multifractal Rényi Dimensions

“…The mutual multifractal spectra represents the relative multifractal analysis introduced by Cole [17] (see also [2,3,56,57]) in the case where s = 0.…”