单调集值测度空间上的Lebesgue与Egoroff型定理  

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

作　　者：开学文 吴健荣[1] 李姣姣[1] 

机构地区：[1]苏州科技学院数理学院,江苏苏州215009

出　　处：《西南师范大学学报（自然科学版）》2015年第8期10-16,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11371013);江苏省高校研究生培养创新工程项目(CXLX13-854);苏州科技学院研究生科研创新计划项目(SKCX13S-048)

摘　　要：对一类取值于m维正欧氏空间子集上的单调集函数,引进了单调集值测度的概念,定义了单调集值测度的连续性.在此基础上,给出了单调集值测度空间上可测函数列几乎处处收敛、依测度收敛、几乎处处一致收敛等概念,并且讨论了它们之间的关系,将经典测度论中的Lebesgue定理、Egoroff定理等重要结论推广到了单调集值测度论中.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 .

关 键 词：单调集值测度 集值集函数 LEBESGUE定理 EGOROFF定理 

分 类 号：O159[理学—数学]