| Mcshane积分的LSRS收敛定理 |
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| 引用本文： | 李伟.Mcshane积分的LSRS收敛定理[J].韩山师范学院学报,2006,27(3):6-9,13. |
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| 作者姓名： | 李伟 |
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| 作者单位： | 集美大学,理学院数学系,福建,厦门,361021 |
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| 摘 要： | 利用函数的局部小黎曼和性质(LSRS)和函数列的一致局部小黎曼和性质(ULSRS), 建立了Mcshane积分的局部小黎曼和收敛定理(定理1)．然后,通过定理2证明了Lebesgue积分的控制收敛定理为该定理的一个推论．
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| 关 键 词： | Mcshane积分 ULSRS 收敛定理 |
| 文章编号： | 1007-6883（2006）03-0006-04 |
| 收稿时间： | 2005-10-16 |
| 修稿时间： | 2005-10-16 |
LSRS Convergence Theorem of Mcshane Integral |
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| LI Wei.LSRS Convergence Theorem of Mcshane Integral[J].Journal of Hanshan Teachers College,2006,27(3):6-9,13. |
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| Authors: | LI Wei |
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| Institution: | Department of Mathematics,School of Science, Jimei University, Xiamen 361021,China |
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| Abstract: | This paper gains the convergence theorem (Theorem 1) of locally small Riemann sum of Mcshane integral, which utilizes the properties of locally small Riemann sum of function(LSRS) and uniformly locally small Riemann sum of sequence of functions(ULSRS). Then it is proved that Lebesgue integral dominated convergence theorem is a corollary of Theorem 1 in Theorem 2. |
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| Keywords: | Mcshane Integral ULSRS Convergence Theorem |
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