Sugeno空间上的波雷尔0-1律及收敛理论  

Borel 0-1 Law and Convergence Theory on Sugeno Space

作　　者：张春琴[1] 张辉[1] 

机构地区：[1]河北大学数学与信息科学学院,河北保定071002

出　　处：《模糊系统与数学》2015年第5期104-108,共5页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61375075);河北省自然科学基金资助项目(A2014201166;F2012201020);河北省教育厅项目(QN20131055)

摘　　要：Sugeno测度是一种模糊测度。在Sugeno空间上提出并证明经典的波雷尔0-1律,同时介绍两种新的收敛概念并讨论这两种收敛之间的关系。这一工作把经典的结论推广到了Sugeno空间,得到了模糊环境下的波雷尔0-1律和相关的收敛理论,扩大了它们的研究范围和应用领域。Sugeno measure is a kind of fuzzy measure. On Sugeno space, the classical Borel 0-1 law will be proposed and proved, and then two new convergence concepts are introduced and the relationships between the two convergence concepts are investigated. The results are natural extensions of the corresponding conclusions of classical theory. The Borel 0-1 law and correlative convergence theory can be obtained in fuzzy environment. Our work generalizes the research and applications of Borel 0-1 law and convergence theory.

关 键 词：Sugeno测度 波雷尔0-1律 收敛 g_λ-随机变量 

分 类 号：O211[理学—概率论与数理统计]