正测度Cantor集与正测度Cantor函数  

POSITIVE MEASURE CANTOR SET AND POSITIVE MEASURE CANTOR FUNCTION

作　　者：李雨哲 王丽 LI Yu-zhe;WANG Li(School of Mathematics and Statistics,Ningxia University,Yinchuan 751601,China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《数学杂志》2023年第3期277-282,共6页Journal of Mathematics

基　　金：2022年宁夏大学研究生教育改革创新与实践项目基金资助。

摘　　要：本文利用类比的方法,将Cantor集上定义的Cantor函数进行了推广.首先给出了正测度Cantor集及正测度Cantor函数的定义;然后通过严格的证明得到了正测度Cantor函数的一些性质,并给出了正测度Cantor函数的一些应用;最后通过实例说明,由于正测度Cantor函数构造的特殊性,可以用来作为一些命题的反例.By using of the method of analogy,Cantor function defining on Cantor set is generalized in this paper.Firstly,the definition of positive measure Cantor set and positive measure Cantor function are given;Secondly,some properties about positive measure Cantor function are obtained by strict proofs,and some applications are proposed;Finally,we find that positive measure Cantor function can be regarded as counter-example owing to its particularity of structure.

关 键 词：CANTOR集 正测度Cantor集 Cantor函数 正测度Cantor函数 

分 类 号：O174.1[理学—数学]