集值模糊测度空间上的Egoroff定理  

The Egoroff theorems in set-valued fuzzy measures space

作　　者：张以欣[1] 王贵君[1] 周立群[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《山东大学学报（理学版）》2010年第5期69-73,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(60974144)

摘　　要：在m维正欧氏空间的子集类上引入一种新的序结构,并依此序结构研究了可测函数列(伪)依集值模糊测度几乎处处收敛,(伪)依集值模糊测度几乎一致收敛等问题。获得了用集值模糊测度刻画函数列的Egoroff定理及其相应的逆定理。A new order structure is introduced on the class of subsets of an m-dimensional positive Euclid space.In the new order structural sense,the relationships between （pseudo-） almost everywhere convergence and （pseudo-） almost uniform convergence in set-valued fuzzy measures are studied.Furthermore,the Egoroff theorems and their corresponding reverse theorems by depicting the sequence of measurable functions with set-valued fuzzy measure are obtained.

关 键 词：集值模糊测度 几乎处处收敛 几乎一致收敛 EGOROFF定理 

分 类 号：O159[理学—数学]