摘要
给出了拓扑空间上的上(下)半连续函数的概念及其等价命题,证明了上(下)半连续函数的一些基本性质,最后介绍常用的Hardy-Littlewood极大函数的下半连续性以及弱下半连续泛函.
In this paper, first we give the concepts of the upper(lower) semicontinuous functions on a topological space and their equivalent propositions, and then show a few basic properties of the upper(lower) semieontinuous functions, finally present the lower semicontinuity of common Hardy-Littlewood maximal functions and weakly semi- continuous functionals.
出处
《淮阴师范学院学报(自然科学版)》
CAS
2012年第2期137-141,共5页
Journal of Huaiyin Teachers College;Natural Science Edition
关键词
拓扑空间
上(下)半连续
极大函数
泛函
topological space
upper (lower) semicontinuous function
maximal function
functional