Riesz定理在证明测度收敛性质中的应用  

The Application of Riesz's Theorem in Proving the Convergence Property of Measure

作　　者：孙秀花 SUN Xiu-hua(Department of Mathematics,Jinzhong University,Jinzhong Shanxi,030600)

机构地区：[1]晋中学院数学学院,山西晋中030600

出　　处：《山西大同大学学报（自然科学版）》2020年第1期31-32,共2页Journal of Shanxi Datong University(Natural Science Edition)

摘　　要：实变函数Riesz定理刻画了几乎处处收敛与依测度收敛的具体关系,通过例子说明该定理在证明测度收敛性质中的应用。最后利用该定理,得出函数列依测度收敛的一个充要条件。Riesz's theorem of real variables describes the specific relationship between almost everywhere convergence and con⁃vergence in measure.The application of this theorem is illustrated by several examples.Finally,by using this theorem,a necessary and sufficient condition for the convergence of function sequence in terms of measure is obtained.

关 键 词：RIESZ定理 依测度收敛 几乎处处收敛 

分 类 号：O174.12[理学—数学]