| 集值模糊测度空间上的Egoroff定理 |
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| 引用本文： | 张以欣,王贵君,周立群.集值模糊测度空间上的Egoroff定理[J].山东大学学报(理学版),2010,45(5):69-73. |
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| 作者姓名： | 张以欣 王贵君 周立群 |
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| 作者单位： | 天津师范大学数学科学学院,天津,300387 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 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。
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| 关 键 词： | 集值模糊测度 几乎处处收敛 几乎一致收敛 Egoroff定理 |
| 收稿时间： | 2009-11-09 |
The Egoroff theorems in set-valued fuzzy measures space |
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| ZHANG Yi-xin,WANG Gui-jun,ZHOU Li-qun.The Egoroff theorems in set-valued fuzzy measures space[J].Journal of Shandong University,2010,45(5):69-73. |
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| Authors: | ZHANG Yi-xin WANG Gui-jun ZHOU Li-qun |
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| Institution: | School of Mathematics Science, Tianjin Normal University, Tianjin 300387, China |
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| 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.
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| Keywords: | set-valued fuzzy measure almost everywhere convergence almost uniform convergence Egoroff theorems |
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