Lusin's theorem on fuzzy measure spaces

7 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 9 regularity and weakly null-additivity. A version of Egoro2’s theorem for the fuzzy measure de3ned on metric spaces is given. An application of Lusin’s theorem to approximation in the mean of measurable function on 11 fuzzy measure spaces is presented. c © 2003 Published by Elsevier Science B.V. 13