Abstract
In this paper, we shall be concerned with evaluation of multifractal Hausdorff measure H-mu(q,t) and multifractal packing measure P-q,P-t (mu) 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.