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Lusin’s theorem on fuzzy measure spaces. (English) Zbl 1046.28012
Summary: We show that weakly null-additive fuzzy measures on metric spaces possess regularity. Lusin’s theorem, which is well-known in classical measure theory, is generalized to fuzzy measure spaces by using the regularity and weak null-additivity. A version of Egoroff’s theorem for the fuzzy measure defined on metric spaces is given. An application of Lusin’s theorem to the approximation in the mean of measurable functions on fuzzy measure spaces is presented.

MSC:
 2.8e+11 Fuzzy measure theory