Lusins theorem on fuzzy measure spaces

AIn this paper, we show that weakly null-additive fuzzy measures on metric spaces possess regularity. Lusinʹs theorem, which is wellknown in classical measure theory, is generalized to fuzzy measure space by using the regularity and weakly null-additivity. A version of Egoroffʹs theorem for the fuzzy measure defined on metric spaces is given. An application of Lusinʹs theorem to approximation in the mean of measurable function on fuzzy measure spaces is presented.