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Subsets Of Positive And Finite Multifractal Measures

Author

Listed:
  • 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)

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.

Suggested Citation

  • Najmeddine Attia & Bilel Selmi, 2024. "Subsets Of Positive And Finite Multifractal Measures," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-8.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:02:n:s0218348x24400048
    DOI: 10.1142/S0218348X24400048
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