Lusin's theorem on fuzzy measure spaces

Abstract

In this paper, 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 space by using the regularity and weakly 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 approximation in the mean of measurable function on fuzzy measure spaces is presented.