On Egoroff's theorems on fuzzy measure spaces

Authors:
Jun Li
Affiliations:
Department of Applied Mathematics, Southeast University, Nanjing 210096, People's Republic of China
Venue:
Fuzzy Sets and Systems - Non-additive measures and random processes
Year:
2003

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Abstract

In this paper, we show that Egoroff's theorem, which is well known in classical measure theory, remains valid for a fuzzy measure without any additional condition. Previous results obtained by Wang Zhenyuan and others are improved. Egoroff's theorem on fuzzy measure spaces is formulated in full generality. Taylor's theorem which concerns convergence almost everywhere in classical measure theory is also extended to fuzzy measure spaces.