Frostman lemmas for Hausdorff measure and packing measure in a product probability space and their physical application

摘要

In this paper, we obtain the analogue of Frostman lemma in a product probability space for Billingsley definition of Hausdorff measure. In the same way, there is a valid result for packing pre-measure. Furthermore, we obtain the representations of dim, and dim,, by means of the analogue of Frostman lemma, and give a technique for showing that A x B is an element of F-1 x F-2 is a fractal with respect to mu = mu(1) x mu(2). (C) 2004 Elsevier Ltd. All rights reserved.