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We prove that for a given normalized compact metric space it can induce aσ-max-superdecomposable measure, by constructing a Hausdorff pseudometric on its power set. We also prove that the restriction of this set function to the algebra of all measurable sets is aσ-max-decomposable measure. Finally we conclude this paper with two open problems.doi:10.1155/2012/701206 fatcat:e7yfhz5u2fbgzcwro7svz2u5na