Abstract
In this paper, we shall be concerned with evaluation of Hewitt-Stromberg measure of Cartesian product sets by means of the measure of their components. This is done by the construction of new multifractal measures, on the Euclidean space R-n, in a similar manner to Hewitt-Stromberg measures but using the class of all n-dimensional half-open binary cubes of covering sets in the definition rather than the class of all balls.