Lusin's theorem on fuzzy measure spaces |
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| Institution: | 1. Department of Engineering, University of Roma Tre, Via V. Volterra 62, 00146 Roma, Italy;2. Department of Engineering, University of Perugia, Via G. Duranti 67, 06125 Perugia, Italy;3. Department of Mathematics and Computer Science, University of Perugia, Via Vanvitelli 1, Perugia 06123, Italy |
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| 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. |
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