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Fuzzy measures on metric spaces. (English) Zbl 0878.28013
Summary: The aim of the present paper is to study the regularity and tightness properties of fuzzy measures on metric spaces. Among other results, we give Lusin’s theorem and Egoroff’s theorem; we also prove the singleton characterization of atom of fuzzy measure, and an algorithm to evaluate the fuzzy integrals of nonnegative measurable functions over an atom and a union of finite disjoint atoms.

MSC:
28E10Fuzzy measure theory
28C15Set functions and measures on topological spaces