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| 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. |
| 关键词: Cantor集 正测度Cantor集 Cantor函数 正测度Cantor函数 |
| DOI： |
| 分类号:O174.1 |
| 基金项目:2022年宁夏大学研究生教育改革创新与实践项目基金资助. |
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| POSITIVE MEASURE CANTOR SET AND POSITIVE MEASURE CANTOR FUNCTION |
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LI Yu-zhe,WANG Li
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| Abstract: |
| 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. |
| Key words: Cantor set positive measure Cantor set Cantor function positive measure Cantor function |
