Packing measures and dimensions on cartesian products

Packing measures Pg(E) and Hewitt-Stromberg measures vg(E) and their relatives are investigated. It is shown, for instance, that for any metric spaces X, Y and any Hausdorff functions f, g vg (X) • Ph (Y) ≤ Pgh (X x Y). The inequality for the corresponding dimensions is established and used for a solution of a problem of Hu and Taylor: If X ⊆ ℝn, then inf {dimpX x Y – dimpY : Y ⊆ ℝn } = lim inf dimB Xn. Corresponding dimension inequalities for products of measures are established.