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J4 ›› 2010, Vol. 45 ›› Issue (5): 69-73.

• 论文 • 上一篇    下一篇

集值模糊测度空间上的Egoroff定理

张以欣,王贵君*,周立群   

  1. 天津师范大学数学科学学院, 天津 300387
  • 收稿日期:2009-11-09 出版日期:2010-05-16 发布日期:2010-05-24
  • 通讯作者: 王贵君(1962-),男, 教授, 研究方向为模糊测度与模糊积分,模糊群理论.
  • 作者简介:张以欣(1986-),女,硕士研究生, 研究方向为模糊测度与积分.Email: xin.xin111@yahoo.com.cn
  • 基金资助:

    国家自然科学基金资助项目(60974144)

The Egoroff theorems in set-valued fuzzy measures space

ZHANG Yi-xin, WANG Gui-jun*, ZHOU Li-qun   

  1. School of Mathematics Science, Tianjin Normal University, Tianjin 300387, China
  • Received:2009-11-09 Online:2010-05-16 Published:2010-05-24

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。

关键词: 集值模糊测度; 几乎处处收敛; 几乎一致收敛; Egoroff定理

Abstract:

 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.
 

Key words: set-valued fuzzy measure; almost everywhere convergence; almost uniform convergence; Egoroff theorems

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