含有不可数个无界变差点的一维连续函数  

1-Dimensional Continuous Functions with Uncountable Unbounded Variation Points

作　　者：梁永顺[1] 张琦[2] LIANG Yongshun;ZHANG Qi(Corresponding author. Institute of Science, Nanjing University of Science and Technology, Nanjing 210094, China;Faculty of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210014, China.)

机构地区：[1]南京理工大学理学院,南京210094 [2]南京航空航天大学理学院,南京210014

出　　处：《数学年刊（A辑）》2018年第2期145-152,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11201230;No.11271182);江苏省自然科学基金(No.BK20161492)的资助

摘　　要：在单位区间[0,1]上构造了图像长度为无穷的一维连续函数.该函数含有不可数个但Lebesgue测度为0的无界变差点.所有无界变差点组成的集合中每一点皆为该集合的聚点.A 1-dimensional continuous function whose graph has infinite length on [0,1]has been constructed. Unbounded variation points of this function are uncountable, while Lebesgue measure of them is 0. All unbounded variation points are accumulation points of the set of unbounded variation points of the function.

关 键 词：CANTOR集 盒维数 变差 图像长度 

分 类 号：O175.29[理学—数学]