The Convergence And Continuity Of Set-valued Functions On Fuzzy Measure Space

In this dissertation, some researches on convergence and continuity of set-valued measurable function on fuzzy measure space are made. The main results of this work consist of three parts, as follows:(1) By using the several continuity of set function, four types of Lebesgue's theorem for set-valued measurable function on monotone measure space are shown, respectively.(2) Standard and pseudo-form of Riesz's theorem for measurable set-valued function on monotone measure space are proved, respectively.(3) Continuity and convergence of set-valued function on fuzzy measure space are discussed. Under the condition of null-additivity of set function, Lusin's theorem of measurable set-valued function on fuzzy measure space is presented.These are further generalization of the related results in real-valued measurable function on fuzzy measure space.