For sequences of measurable functions on a set-valued fuzzy measure space, the concepts of pseudo almost everywhere convergence, pseudo almost uniformly convergence, and pseudo-convergence in measure are introduced. Then, Egoroff’s theorem, Lebesgue’s theorem, and Riesz’s theorem are generalized from real-valued fuzzy measure spaces onto set-valued fuzzy measure spaces.
Fuzzy analysis Set-valued fuzzy measure Measurable function Convergence theorem
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Jianrong Wu has been supported by National Natural Science Foundation of China (No. 11371013). The authors acknowledge the reviewer’s comments and suggestions very much, which are valuable in improving the quality of our manuscript.
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Both authors declare that they have no conflict of interest.
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This article does not contain any studies with human participants or animals performed by any of the authors.
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