Abstract
The pseudometric generating property of non-additive set functions also plays an important role as the autocontinuity in fuzzy measure theory (Jiang, Ph.D. Thesis, Chiba University, 1996; Wang and Klir, Fuzzy Measure Theory, Plenum Press, New York, 1992). A further research on this property has been presented in Jiang et al. (Fuzzy Sets and Systems, 1998). The aim of this paper is to prove the Egoroff's theorem and Lusin's theorem for measurable functions on metric spaces hold for those fuzzy measures with the exhaustivity and pseudometric generating property.
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