  Using methods from nonstandard analysis, we define a nonstandard Minkowski
dimension which exists for all bounded sets and which has the property that
$\dim(A\times B) = \dim(A) + \dim(B)$.That is, our new dimension is
product-summable. To illustrate our theorem we generalize an example of
Falconer's to show that the standard upper Minkowski dimension, as well as the
Hausdorff dimension, are not product-summable. We also include a method for
creating sets of arbitrary rational dimension.
