Rectangular functions and fractal measures, a general discussion of measures of Cartesian product sets

Abstract

In the present work, we investigate the mixed generalized Hausdorff and packing measures. We emphasize the significance of these measures in analyzing the geo- metric and dimensional properties of product sets. Our study provides a thorough and detailed discussion on the measurement of product sets in general metric spaces (X, ρ). Additionally, we will explore the 0 − ∞ case under a geometric condition on X, which has been excluded in several previous studies.