Remarks on the mutual singularity of multifractal measures

Selmi, Bilel

doi:10.22199/issn.0717-6279-2021-01-0005

Cited by 6 publications

(2 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In our work, we get such coincidence without restricting to compact metric spaces. See also [28,64]. In [27], the authors applied the mixed multifractal analysis of measures to estimate the Rényi dimension relative to a couple of measures where the product of such measures is controlled by the diameter/radius of the coverings.…”

Section: On the Utility Of Mixed Multifractal Analysis And Motivationsmentioning

confidence: 99%

A mixed multifractal analysis for quasi Ahlfors vector-valued measures

Farhat¹,

Mabrouk²

2021

Preprint

View full text Add to dashboard Cite

The multifractal formalism for measures in its original formulation is checked for special classes of measures such as doubling, self similar, and Gibbs-like ones. Out of these classes, suitable conditions should be taken into account to prove the validity of the multifractal formalism. In the present work, a large class of measures satisfying a weak condition known as quasi Ahlfors is considered in the framework of mixed multifractal analysis. A joint multifractal analysis of finitely many quasi Ahlfors probability measures is developed. Mixed variants of multifractal generalizations of Hausdorff and packing measures, and corresponding dimensions are introduced. By applying convexity arguments, some properties of these measures and dimensions are established. Finally, an associated multifractal formalism is introduced and proved to hold for the class of quasi Ahlfors measures.

show abstract

Section: On the Utility Of Mixed Multifractal Analysis And Motivationsmentioning

confidence: 99%

A mixed multifractal analysis for quasi Ahlfors vector-valued measures

Farhat¹,

Mabrouk²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…This means that, we somehow forget the geometric structure of X and focus instead on the properties of the measure µ. The set X is thus partitioned into α-level sets X µ (α) relatively to the regularity exponent of µ (see for example [1,2,9,21,22,23,27,31,39,40,42,43]). In the present work, we will be interested to the development of a mixed multifractal analysis of finitely many measures.…”

Section: Introductionmentioning

confidence: 99%

On the mixed multifractal formalism for vector-valued measures

Selmi

Mabrouk

2022

Proyecciones (Antofagasta)

Self Cite

View full text Add to dashboard Cite

The multifractal formalism for vector-valued measures holds when-ever the existence of corresponding Gibbs-like measures, supported on the singularities sets holds. We tried through this article to improve a result developed by Menceur et al. in [29] and to suggest a new sufficient condition for a valid mixed multifractal formalism for vector-valued measures. We describe a necessary condition of validity for the formalism which is very close to the sufficient one.

show abstract

On the mutual singularity of Hewitt–Stromberg measures for which the multifractal functions do not necessarily coincide

Douzi

Selmi

2021

Ricerche mat

View full text Add to dashboard Cite

Remarks on the mutual singularity of multifractal measures

Cited by 6 publications

References 10 publications

A mixed multifractal analysis for quasi Ahlfors vector-valued measures

A mixed multifractal analysis for quasi Ahlfors vector-valued measures

On the mixed multifractal formalism for vector-valued measures

On the mutual singularity of Hewitt–Stromberg measures for which the multifractal functions do not necessarily coincide

Contact Info

Product

Resources

About