| 关于各种收敛性关系的若干反例及两个新的定理 |
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| 引用本文： | 程毕陶. 关于各种收敛性关系的若干反例及两个新的定理[J]. 曲靖师专学报, 2011, 0(3): 19-23 |
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| 作者姓名： | 程毕陶 |
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| 作者单位： | 曲靖师范学院数学与信息科学学院,云南曲靖655011 |
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| 基金项目： | 曲靖师范学院青年项目“非线性分析中的一类基尔霍夫型问题的变分方法研究”（2009QN018）阶段性研究成果 |
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| 摘 要： | 主要研究了Lp（p≥1）空间中的强收敛（依范数收敛）、弱收敛与几乎处处收敛、依测度收敛、一致收敛之间的关系,并举出了若干反例;进一步对函数序列或测度空间作某些假设,得到了一些肯定的蕴涵关系与重要的结论.
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| 关 键 词： | 强收敛 弱收敛 几乎处处收敛 依测度收敛 一致收敛 |
Opposite examples about relationships between convergences and two theorems |
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| Cheng Bitao. Opposite examples about relationships between convergences and two theorems[J]. , 2011, 0(3): 19-23 |
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| Authors: | Cheng Bitao |
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| Affiliation: | Cheng Bitao(School of Mathematics and Information Science,Qujing Normal University,Qujing Yunnan 655011,P.R.China) |
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| Abstract: | The aim of this paper is to study the relationships between strong convergence（convergence in norm）、weak convergence、uniform convergence、almost everywhere convergence and convergence in measure in LP（P≥1）,meanwhile we give some opposite examples,moreover we make the suppose about the measure space and function sequence,and obtain their implying relationships and important conclusions. |
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| Keywords: | strong convergence weak convergence uniform convergence almost everywhere convergence convergence in measure implying |
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