| 收敛函数列的一个性质 |
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| 引用本文： | 戚民驹.收敛函数列的一个性质[J].安徽大学学报(自然科学版),2008,32(2):8-11. |
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| 作者姓名： | 戚民驹 |
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| 作者单位： | 上海电机学院,数理系,上海,200240 |
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| 摘 要： | 给出函数间断度定义、本性间断点定义及几乎处处连续的本性函数定义,由勒贝格可测函数的本性定理将收敛的几乎处处连续的本性函数列的上、下确界函数本性化,证明收敛的几乎处处连续的本性函数列的无界点集的闭包S∞为零集.
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| 关 键 词： | 上、下确界函数 勒贝格零集 几乎处处连续的本性函数 近似连续点 |
| 文章编号： | 1000-2162(2008)02-0008-04 |
| 修稿时间： | 2007年9月16日 |
A property on the sequence of convergent function |
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| QI Min-ju.A property on the sequence of convergent function[J].Journal of Anhui University(Natural Sciences),2008,32(2):8-11. |
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| Authors: | QI Min-ju |
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| Abstract: | The article gave the definition of the degree of the discontinuity,the definition of the essential discontinuous point and the definition of the essential functions which are continuous almost everywhere,the supremum and infimum functions of the sequence of convergent almost everywhere continuous essential function were naturalized by the natural disposition theorem on Lebesgue measurable function.The closure of boundless-point-set,which is zero set,of convergent almost everywhere continuous essential function sequence was proved. |
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| Keywords: | supremum and infimum functions Lebesgue zero set the essential functions which are continuous almost everywhere approximately continuous point |
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