| 关于上(下)半连续函数的讨论 |
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| 引用本文： | 尚朝阳.关于上(下)半连续函数的讨论[J].淮阴师范学院学报(自然科学版),2012(2):137-141. |
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| 作者姓名： | 尚朝阳 |
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| 作者单位： | 南京财经大学应用数学学院 |
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| 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.
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| 关 键 词： | 拓扑空间 上(下)半连续 极大函数 泛函 |
Discussions on the Upper(Lower) Semicontinuous Functions |
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| SHANG Zhao-yang.Discussions on the Upper(Lower) Semicontinuous Functions[J].Journal of Huaiyin Teachers College(Natrual Science Edition),2012(2):137-141. |
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| Authors: | SHANG Zhao-yang |
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| Institution: | SHANG Zhao-yang(School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing Jiangsu 210046) |
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| Abstract: | 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) semicontinuous functions,finally present the lower semicontinuity of common Hardy-Littlewood maximal functions and weakly semicontinuous functionals. |
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| Keywords: | topological space upper(lower) semicontinuous function maximal function functional |
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