SUBSETS OF POSITIVE AND FINITE MULTIFRACTAL MEASURES

Najmeddine Attia and Bilel Selmi ()
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Najmeddine Attia: Department of Mathematics and Statistics, College of Science, King Faisal University, P. O. Box 400, Al-Ahsa 31982, Saudi Arabia
Bilel Selmi: Analysis, Probability and Fractals Laboratory LR18ES17, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5000 Monastir, Tunisia

FRACTALS (fractals), 2024, vol. 32, issue 02, 1-8

Abstract: Sets of infinite multifractal measures are awkward to work with, and reducing them to sets of positive finite multifractal measures is a very useful simplification. The aim of this paper is to show that the multifractal Hausdorff measures satisfy the “subset of positive and finite measure†property. We apply our main result to prove that the multifractal function dimension is defined as the supremum over the multifractal dimension of all Borel probability measures.

Keywords: Hausdorff Measure; Hausdorff Dimension; Net Measure; Subset of Positive and Finite Measure (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400048

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