| 控制收敛定理的推广及其应用 |
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| 引用本文： | 黄祖达,李应求,肖宏芳,张敏.控制收敛定理的推广及其应用[J].湖南文理学院学报(自然科学版),2013(2):13-15. |
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| 作者姓名： | 黄祖达 李应求 肖宏芳 张敏 |
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| 作者单位： | 湖南文理学院 数学与计算科学学院，湖南 常德，415000;长沙理工大学 数学与计算科学学院，湖南长沙，410076;常德财经学校，湖南 常德，415000 |
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| 基金项目： | 国家自然科学基金（10771021） |
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| 摘 要： | 基于叶果罗夫定理,考虑Lebesgue积分序列的收敛性,证明了一致绝对连续可积函数序列的处处收敛性,通过分析Sobolev空间逼近函数列的性质,发现了它的一致绝对连续性以及相应积分序列的收敛性,证明了Sobolev空间中的函数可以被一致绝对连续函数列逼近.因此只要函数列一致绝对连续可积,就足以保证积分序列的收敛,最后举例进行了说明.
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| 关 键 词： | Lebesgue积分序列 一致绝对连续 收敛 |
Generalized dominated convergence principle and its application |
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| HUANG Zu-da,LI Yin-qiu,XIAO Hong-fang,ZHANG Min.Generalized dominated convergence principle and its application[J].Journal of Hunan University of Arts and Science:Natural Science Edition,2013(2):13-15. |
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| Authors: | HUANG Zu-da LI Yin-qiu XIAO Hong-fang ZHANG Min |
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| Institution: | 1. College of Mathematics and Computer Science, Hunan University of Arts and Science, Changde 415000, China; 2. College of Mathematics and Computer Science, Changsha University of Science and Technology, Changsha 410076, China; 3. Changde Finance School, Changde 415000, China) |
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| Abstract: | Based on the Eropob-theorm, the article considers sequences of Lebesgue imegrable functions, and proves that the a.e. convergence of a sequence of uniformly absolute continuously integrable functions implies the convergence of the sequence of their integration, anlysises deeply that Sobolev-space function＇s characters,discovers that the uniformly absolute continuous and coresponding convergence of an integration sequence, and further proves that any function in Sobolev-space can be approximated by a sequence of uniformly absolute continuously integrable functions. The concolusion of the article is that a sequence of uniformly absolute continuously integrable functions implies the convergence of the sequence .An examples is given to illustrate their applications. |
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| Keywords: | Lebesgue integration sequence uniformly absolutely continuous convergence |
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