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.
作者
梁永顺
张琦
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.)
出处
《数学年刊（A辑）》
CSCD
北大核心
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
