On the convergence of measurable set-valued function sequence on fuzzy measure space

Abstract

In this paper we first discuss the measurable projection theorem on fuzzy measure space, and in this framework the characterization theorem with respect to measurability of a set-valued function is given. By means of the asymptotic structural characteristics of fuzzy measure, we discuss four forms of generalization for both Lebesgue's theorem, Riesz's theorem, and Egoroff's theorem, respectively. The relation between convergence of measurable set-valued function sequence and that of corresponding measurable real-valued function sequence are also discussed.