| 含有不可数个无界变差点的一维连续函数 |
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| 引用本文： | 梁永顺,张琦. 含有不可数个无界变差点的一维连续函数[J]. 数学年刊A辑(中文版), 2018, 39(2): 145-152 |
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| 作者姓名： | 梁永顺 张琦 |
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| 作者单位： | 南京理工大学理学院;南京航空航天大学理学院 |
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| 基金项目： | 本文受到国家自然科学基金(No.11201230, No.11271182)和江苏省自然科学基金(No.BK20161492)的资助. |
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| 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.
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| 关 键 词： | Cantor集 盒维数 变差 图像长度 |
| 收稿时间： | 2016-05-27 |
| 修稿时间： | 2017-05-17 |
1-Dimensional Continuous Functions with Uncountable Unbounded Variation Points |
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| LIANG Yongshun and ZHANG Qi. 1-Dimensional Continuous Functions with Uncountable Unbounded Variation Points[J]. Chinese Annals of Mathematics, 2018, 39(2): 145-152 |
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| Authors: | LIANG Yongshun and ZHANG Qi |
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| Affiliation: | Corresponding author. Institute of Science, Nanjing University of Science and Technology, Nanjing 210094, China. and Faculty of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210014, China. |
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| Abstract: | 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 pointsare accumulation points of the set of unbounded variation points of the function. |
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| Keywords: | Cantor set Box dimension Variation Length of graph |
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