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.
作者
孙秀花
SUN Xiu-hua(Department of Mathematics,Jinzhong University,Jinzhong Shanxi,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)
关键词
RIESZ定理
依测度收敛
几乎处处收敛
Riesz's theorem
convergence in measure
convergence almost everywhere
