| 函数序列收敛与图距离收敛的等价关系 |
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| 引用本文： | 霍永亮,李晓莉.函数序列收敛与图距离收敛的等价关系[J].榆林高等专科学校学报,2003,13(3):7-10. |
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| 作者姓名： | 霍永亮 李晓莉 |
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| 作者单位： | [1]榆林学院数学系，陕西榆林719000 [2]长安大学理学院，陕西西安710064 |
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| 摘 要： | 通过给出函数序列收敛与函数序列的图以图距离收敛的等价关系，证明了三种函数序列收敛的等价性，讨论了三种函数序列收敛与epi—收敛之间的强弱关系。
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| 关 键 词： | 函数序列 收敛性 图距离 连续性 图范数 等价关系 |
| 文章编号： | 1008-3871(2003)03-0007-03 |
The equivalence relation between the convergence of function sequence and that of the graph-distance |
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| HUO Yong - Hang LI Xiao - li.The equivalence relation between the convergence of function sequence and that of the graph-distance[J].Journal of Yulin College,2003,13(3):7-10. |
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| Authors: | HUO Yong - Hang LI Xiao - li |
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| Abstract: | The equivalence relation between the convergence of a function sequence and that of a function sequence in manner of graph - distance is presented. The equivalence relations among three types of convergences of function sequences are also proved. The strength - weakness relation between the three types of function sequence convergences and the epi - convergences is discussed. |
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| Keywords: | graph - distance epi - convergence uniform convergence to a continuouous limit continus convergence convergence of equicontinuous functions |
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