A New Upper Bound of Hausdorff Measure of the Product of the Cantor Set with Itself

Let E be the product of the Middle Third Cantor set with itself we prove that the minimal value of the inverse density of a special class of balls can be attained,denoted by h(s)(E),which gives an upper bound of the Hausdorff measure of E in the nature of things. We also introduce an approximation method for calculating the exact value of h(s)(E). And then we get a new upper bound of the Hausdorff measure of E.