On Lebesgue Theorem and Egoroff Theorem on Monotone Set-valued Measure Spaces

Key words: 
• monotone set-valued measure，set-valued set function，Lebesgue Theorem，Egoroff Theorem /
•  /
•  /

Abstract: As a special kind of monotone set function taking value in the power set of an m‐dimension posi‐tive Euclid space ,the concept of monotone set‐valued measure has been introduced ,and its different kinds of continuity defined .On these bases ,for a sequence of measurable functions defined on monotone set‐val‐ued measure spaces ,some convergence concepts such as almost everyw here convergence ,convergence in measure ,almost uniform convergence everywhere are given .The relationships among these convergences have been discussed .Some important results such as Lebesgue Theorem and Egoroff Theorem in the clas‐sical measure theory are generalized to monotone set‐valued measure theory .