| 可测集的一个充分必要条件 |
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| 引用本文： | 郑利凯.可测集的一个充分必要条件[J].湖北民族学院学报(哲学社会科学版),2011,29(1). |
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| 作者姓名： | 郑利凯 |
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| 作者单位： | 内蒙古民族大学数学学院,内蒙古,通辽,028000 |
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| 基金项目： | 内蒙古自治区自然科学基金 |
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| 摘 要： | 判断Ra中的点集是否可测是实变函数研究的重要内容.通过卡拉泰奥多里条件,研究给出了Ra中的点集可测的一个充要条件,并用这个结论证明了Cantor集是可测集.
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| 关 键 词： | 可测集 充要条件 Cantor集 |
A Necessary and Sufficient Condition for Measurable Sets |
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| ZHENG Li-kai.A Necessary and Sufficient Condition for Measurable Sets[J].Journal of Hubei Institute for Nationalities(Natural Sciences),2011,29(1). |
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| Authors: | ZHENG Li-kai |
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| Institution: | ZHENG Li-kai (College of Mathematics,Inner Mongolia University for the Nationalities,Tongliao 028000,China) |
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| Abstract: | Judging whether a set in Rn is measurable is a important content in the real variable function course.On the basis of the Caratheodory condition,a necessary and sufficient condition for measurable sets in Rn has been given.Using the conclusion,the paper proves that Cantor set is measurable. |
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| Keywords: | measurable set necessary and sufficient condition Cantor set |
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