| | | | | 关于Fuzzy测度几个重要结果的证明 | | | 熊启才;周建设 | | | 在Fuzzy测度理论中,M.Sugeno定义了Fuzzy测度并提出了“几乎处处收敛”的概念.文[2~4,6,7]研究了Fuzzy测度的重要性质,本文相应地给出并证明了Fuzzy测度关于依测度收敛的几个重要结果.
【作者单位】：陕西理工学院数学系 陕西汉中723000(熊启才);玉溪师范学院数学系 云南玉溪653100(周建设)
【关键词】：Fuzzy测度;依测度收敛;lebesgue定理;Rieze定理
【基金】：陕西理工学院科研基金项目,编号:SLG04020
【分类号】：O159
【DOI】：CNKI:ISSN:1009-9506.0.2007-03-003
【正文快照】：
1定义定义1.1[1]设X是非空集合,A*是X的子集族构成的σ代数,映射μ:A*→[0,∞]称为Fuzzy测度,如果μ满足下列条件:(FM1).μ()=0;(FM2).若A B,则μ(A)μ(B);(FM3).若A1 A2…An…,An∈A*,则μ(∞∪n=1An)=limn→∞μ(An);(FM4).若A1 A2…An…,An∈A*,存在n0,使得μ(An0)<∞,则μ(∩∞n=1An)=limn→∞μ(An).则(X,A*,μ)称为Fuzzy测度空间.定义1.2[2]若对任何E,F∈A*,μ(F)=0,μ(E∪F)=μ(E),称Fuzzy测度μ为零可加的.定义1.3[2]若对一切A∈A*及一切满足μ(Bn)→0的{Bn}A*,均有μ(A∪Bn)→μ(A)(n→∞)或μ(A-Bn)→μ(… | | |  推荐 CAJ下载  PDF下载 | | | CAJViewer7.0阅读器支持所有CNKI文件格式，AdobeReader仅支持PDF格式 | | | | The Demonstration of a Few Important Results of Fuzzy Measure | | | XIONG Qi-cai1 ZHOU Jian-she2(1.Department of Mathematics;Shaanxi University of Technology;Hanzhong;Shaanxi 723000;2.Department of Mathematics;Yuxi Teachers College;Yuxi;Yunnan 653100) | | | In the theory of Fuzzy measure,M.sugeno gives a definition of Fuzzy measure and puts forwards the concept of 'almost every convergence'.Papers [2～4,,6,7]studied some important properties of the Fuzzy measure.In this paper,we give not only a few important results about convergence in measure of Fuzzy measure but also a demonstration of these results.
【Keyword】：Fuzzy measure;convergence in measure;Lebesgue Theorem;Riesz Theorem |
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