On Decomposable Measures Induced by Metrics

Abstract

We prove that for a given normalized compact metric space it can induce a $\sigma$-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 a $\sigma$-max-decomposable measure. Finally we conclude this paper with two open problems.