L^p空间上依测度收敛与依范数收敛的关系  

The Relationship Between Convergence in Measure and Convergence in Norm in L^p Space

作　　者：赵华新[1] 张萍[1] 

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《天津师范大学学报（自然科学版）》2006年第1期52-54,共3页Journal of Tianjin Normal University：Natural Science Edition

基　　金：陕西省自然科学基金资助项目(2002B21)

摘　　要：Lp空间中的函数列{nf(x)}依测度收敛与依范数收敛的基本关系是:依范数收敛可推出依测度收敛,但逆命题不成立.本文在依测度收敛的基础上,加上必要的条件fn(x)≤fn+1(x)a.e于E且‖fn‖p→‖f‖p或为{f,f1,f2,…}为一致可积族,使得依测度收敛能够推出依范数收敛.The fundamental relationship between convergence in measure and convergence in norm of sequence of functions {fn（x） } in L^p is that convergence in norm is able to deduce convergence in measure, however, the inverse proposition is false. This paper shows convergence in measure, together with necessary condition fn（x） ≤fn＋1 （x） a. e in E or {f,f1 ,f2,… } uniformly integrable functions can deduce convergence in norm.

关 键 词：L^P空间 依测度收敛 依范数收敛 

分 类 号：O177[理学—数学]