Book Review: Integral, probability, and fractal measures

Olsen, L.

doi:10.1090/s0273-0979-00-00878-8

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On the Utility Of Mixed Multifractal Analysis And Motivations1

Introduction1

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2021

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Cited by 1 publication

(2 citation statements)

References 40 publications

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“…The last assumption is already assumed in [13], [10], [11], [48], [49], [50], [51], [52], [53], [55] but unfortunately not in [2] and [20]. When assuming that the measure is quasi-Ahlfors, this assumption is not necessary and may be replaced by the original one in [13] on µ-ε-coverings.…”

Section: On the Utility Of Mixed Multifractal Analysis And Motivationsmentioning

confidence: 99%

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A mixed multifractal analysis for quasi Ahlfors vector-valued measures

Farhat¹,

Mabrouk²

2021

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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.

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Section: On the Utility Of Mixed Multifractal Analysis And Motivationsmentioning

confidence: 99%

“…Such a mixed analysis has been generating a great attention recently and thus proved to be powerful in describing the local behavior of measures especially fractal ones. (See [9], [10], [11], [49], [50], [52], [53], [54], [60], [69], [70], [71], [73], [74], [75], [76]).…”

Section: Introductionmentioning

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

Book Review: Integral, probability, and fractal measures

Cited by 1 publication

References 40 publications

A mixed multifractal analysis for quasi Ahlfors vector-valued measures

A mixed multifractal analysis for quasi Ahlfors vector-valued measures

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