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

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 dimμ and dimμ by means of the analogue of Frostman lemma, and give a technique for showing that A×B∈F1×F2 is a fractal with respect to μ=μ1×μ2.