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
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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。
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关键词:
- 单调集值测度 /
- 集值集函数 /
- Lebesgue定理 /
- Egoroff定理
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 . -
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