浅析几类连续函数的关系  

Analysis on the Relationship of Several Kinds of Continuous Functions

作　　者：江添辉 王维克 JIANG Tianhui;WANG Weike(Zhiyuan College,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学致远学院,上海200240

出　　处：《大学数学》2025年第1期110-116,共7页College Mathematics

摘　　要：主要分析连续函数、一致连续函数、Lipschitz连续函数、Holder连续函数和绝对连续函数这五类连续函数之间的关系.首先分析连续函数、一致连续函数、Lipschitz连续函数和绝对连续函数之间的包含关系,接着分析Holder连续函数与其它连续函数的关系,最后进行总结,给出这五类连续函数的关系图.We mainly analyze the relationship between continuous functions,uniformly continuous functions,Lipschitz continuous functions,Holder continuous functions,and absolutely continuous functions.Firstly,the containment relationship among continuous functions,uniformly continuous functions,Lipschitz continuous functions,and absolutely continuous functions are analyzed.Then we analyze the relationship between the Holder continuous function and other continuous functions,and finally summarize and give the relationship diagrams of these five types of continuous functions.

关 键 词：连续函数 一致连续 LIPSCHITZ连续 HOLDER连续 绝对连续 

分 类 号：O171[理学—数学]