Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024



Commun. Korean Math. Soc. 2022; 37(4): 1073-1097

Online first article September 16, 2022      Printed October 31, 2022

Copyright © The Korean Mathematical Society.

Note on the multifractal measures of Cartesian product sets

Najmeddine Attia, Rihab Guedri, Omrane Guizani

University of Monastir; University of Monastir; University of Monastir


In this paper, we shall be concerned with evaluation of multifractal Hausdorff measure ${\mathcal H}^{q,t}_\mu$ and multifractal packing measure ${\mathcal P}^{q,t}_\mu$ of Cartesian product sets by means of the measure of their components. This is done by investigating the density result introduced in \cite{Olsen95}. As a consequence, we get the inequalities related to the multifractal dimension functions, proved in \cite{Olsen96}, 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.

Keywords: Multifractal Hausdorff measure, multifractal packing measure, product sets

MSC numbers: Primary 28A78, 28A80

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