关于上(下)半连续函数的讨论

Discussions on the Upper(Lower) Semicontinuous Functions

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.