On the multifractal measures and dimensions of image measures on a class of Moran sets

Najmeddine Attia and Bilel Selmi

Chaos, Solitons & Fractals, 2023, vol. 174, issue C

Abstract: On a Moran set meeting the strong separation requirement, we examine a family of multifractal Hausdorff and packing measures and dimensions in this study. Let φ∗π be the image measure of ergodic Borel probability measure π and measurable function φ. Entropy is used to calculate the formula for the dimension of the multifractal measure of φ∗π. Moreover, some statistical interpretations, on a class of Moran sets, of the dimensions and corresponding geometrical measures are also supported. Finally, a specific illustration of a measure that satisfies the aforementioned criteria is created.

Keywords: Multifractal Hausdorff measure; Multifractal packing measure; Densities; Doubling measures; Moran sets; Image of measures (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007191

DOI: 10.1016/j.chaos.2023.113818

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