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On decomposable measures induced by metrics. (English) Zbl 1252.28001
Summary: 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.

MSC:
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
28A60 Measures on Boolean rings, measure algebras
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
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