a1 Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS
We show that for arbitrary metric spaces X and Y the following dimension inequalities hold:
where ‘dim’ denotes Hausdorff dimension and ‘Dim’ denotes packing dimension. The main idea of the proof is to use modified constructions of the Hausdorff and packing measure to deduce appropriate inequalities for the measure of X × Y.
(Received December 19 1994)
(Revised April 28 1995)