| 函数列的黎曼积分极限定理的应用 |
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| 引用本文： | 邢家省,张愿章.函数列的黎曼积分极限定理的应用[J].数学学习,2010(6):50-53. |
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| 作者姓名： | 邢家省 张愿章 |
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| 作者单位： | [1]北京航空航天大学数学与系统科学学院,北京 100191 [2]华北水利水电学院,郑州 450011 |
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| 基金项目： | 基金项目：国家自、然科学基金（10771011）. |
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| 摘 要： | 利用函数列的极限理论方法,研究函数列积分极限中积分和极限可交换次序的问题.对一致收敛的可积函数列给出积分的极限定理,对一致有界局部一致收敛函数列给出积分控制收敛定理,通过大量实例表明该理论的意义所在.
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| 关 键 词： | 函数列的极限 函数列积分极限 黎曼积分控制收敛定理 |
The Limit Problem of Functional Sequence's Riemann-integral |
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| XING Jia Sheng,ZHANG Yuan Zhang.The Limit Problem of Functional Sequence's Riemann-integral[J].Studies In College Mathematics,2010(6):50-53. |
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| Authors: | XING Jia Sheng ZHANG Yuan Zhang |
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| Institution: | 1. Department of Mathematics, LMIB of the Ministry of Education, Beihang University, Beijing, 100191, PRC 2. North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou, 450011, PRC) |
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| Abstract: | By using the limit theorem of functional sequence, we research problems of the integral and limit exchangeable order about the functional sequence＇s integral. We give the limit theorem for the integral functional sequence with uniform convergence. And for the functional sequence with uniform sector and local uniform convergence, we also give the integral dominated convergence theorem. Through the settlement and application of examples, the theory shows its necessity and power. |
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| Keywords: | he limits of functions the limit of functional sequence＇s integral Riemann-Integral Dominated Convergence Theorem |
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