Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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NOTE ON THE MULTIFRACTAL MEASURES OF CARTESIAN PRODUCT SETS

  • Attia, Najmeddine (Analysis, Probability and Fractals Laboratory LR18ES17 Department of Mathematics Faculty of Sciences of Monastir University of Monastir) ;
  • Guedri, Rihab (Analysis, Probability and Fractals Laboratory LR18ES17 Department of Mathematics Faculty of Sciences of Monastir University of Monastir) ;
  • Guizani, Omrane (Analysis, Probability and Fractals Laboratory LR18ES17 Department of Mathematics Faculty of Sciences of Monastir University of Monastir)
  • Received : 2021.10.21
  • Accepted : 2022.02.07
  • Published : 2022.10.01
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Abstract

In this paper, we shall be concerned with evaluation of multifractal Hausdorff measure 𝓗q,t𝜇 and multifractal packing measure 𝓟q,t𝜇 of Cartesian product sets by means of the measure of their components. This is done by investigating the density result introduced in [34]. As a consequence, we get the inequalities related to the multifractal dimension functions, proved in [35], by using a unified method for all the inequalities. Finally, we discuss the extension of our approach to studying the multifractal Hewitt-Stromberg measures of Cartesian product sets.

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References

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