| 论极限、连续与Riemann可积性 |
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| 引用本文： | 张鸣. 论极限、连续与Riemann可积性[J]. 郧阳师范高等专科学校学报, 2001, 21(3): 3-4,6 |
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| 作者姓名： | 张鸣 |
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| 作者单位： | 郧阳师范高等专科学校,数学系,湖北,丹江口,442700 |
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| 摘 要： | 在有限区间I上定义的有界函数f(x)为Riemann可积的充要条件是f(x)在I上α.e.连续,因此几乎处处有有限的极限.相反,由极限(单侧极限)几乎处处存在也可断言f(x)在I上a.e.连续,因而是Riemann可积的.
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| 关 键 词： | 极限 a.e.连续 Riemann可积性 |
| 文章编号： | 1008-6072(2001)03-0003-02 |
| 修稿时间： | 2001-03-14 |
On Limit、 Continuum and Riemann Integrability |
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| ZHANG Ming. On Limit、 Continuum and Riemann Integrability[J]. Journal of Yunyang Teachers College, 2001, 21(3): 3-4,6 |
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| Authors: | ZHANG Ming |
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| Abstract: | A bounded function f(x) defined on [ a,b] is Riemann integrable if and only if it is continuous a. e., therefore, the limits of f(x) is existence a .e., conversly, if a bounded function f(x) defined on [ a,b] which has limits or left (right) limits a. e. is continuous a. e. and Riemann integrable. |
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| Keywords: | limit continuous a. e. Riemann integrability. |
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