ABSTRACT
The natural conjecture is that the Hausdorff dimension of a Cartesian product A × B is the sum of the dimension of A and the dimension of B. In general that is false ([2]; a more elementary example is in [8, Theorem 5.11]). The correct result for Hausdorff dimension of general Cartesian products is just an inequality dim A × B ≥ dim A + dim B. The original Proofs of this relied on density results ([2], [5], Selection 13), and do not apply directly to the case of sets of infinite measure. In this selection, J. M. Marstrand proposed another method to prove these product theorems, and the requisite density results.
