| 关于C1-积分 |
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| 引用本文： | 赵大方.关于C1-积分[J].数学杂志,2011,31(5). |
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| 作者姓名： | 赵大方 |
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| 作者单位： | 湖北师范学院数学与统计学院,湖北黄石,435002 |
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| 基金项目： | Supported by Science Foundation of Hubei Normal University (2007D41) |
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| 摘 要： | 本文利用Riemann和的Moore-Smith极限来定义并研究C1-积分.利用C1-积分的有关性质,讨论了C1-积分与C-积分之间的关系,并给出了一个零测度集特征函数C1-可积的充要条件,从而推广了文献5]的有关结论.
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| 关 键 词： | C-积分 C1-积分 特征函数 |
ON THE C1-INTEGRAL |
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| ZHAO Da-fang.ON THE C1-INTEGRAL[J].Journal of Mathematics,2011,31(5). |
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| Authors: | ZHAO Da-fang |
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| Institution: | ZHAO Da-fang (School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China) |
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| Abstract: | In this article,we define and study the C1-integral by means of Moore-Smith limit of the Riemann sums by using the directed set.Using properties of C1-integral,we discuss the relation between C1-integral and C-integral and give a sufficient and necessary condition for C1-integrability of the characteristic function of a set E of measure zero.This work extends the results in5]. |
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| Keywords: | C-integral C1-integral characteristic function |
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