| G可积函数的Lebesgue可测性 |
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| 引用本文： | 李毅侠,董新汉,王体福.G可积函数的Lebesgue可测性[J].应用数学学报,2007,30(2):327-333. |
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| 作者姓名： | 李毅侠 董新汉 王体福 |
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| 作者单位： | 1. 湘南学院数学系,郴州,423000
2. 湖南师范大学数学与计算机科学学院,长沙,410081 |
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| 基金项目： | 国家自然科学基金;湖南省自然科学基金 |
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| 摘 要： | Botsko在连续和可导的知识基础上推广了Riemann积分,得到了一种新的积分,称为G积分．G积分既不同于Riemann积分也不同于Lebesgue积分．本文通过对G积分的研究,得到了G可积函数一定Lebesgue可测,从而有界G可积函数一定Lebesgue可积;同时我们还证明了这两个积分值相等．
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| 关 键 词： | G可积 Lebesgue可测 Lebesgue可积 |
| 修稿时间： | 2005-12-312006-01-18 |
The Lebesgue Measurability of the G Integrable Function |
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| LI YIXIA,DONG XINHAN,WANG TIFU.The Lebesgue Measurability of the G Integrable Function[J].Acta Mathematicae Applicatae Sinica,2007,30(2):327-333. |
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| Authors: | LI YIXIA DONG XINHAN WANG TIFU |
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| Institution: | 1Department of Mathematics of Xiangnan University, Chenzhou 423000;2College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081 |
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| Abstract: | On the basis of the concepts of continuity and the derivative,Botsko generalized the Riemann integral and obtained a new type integral which is called the G integral.The G integral is different from the Riemann integral and the Lebesgue integral.In this paper,we study the G integral and obtain that a G integrable function is Lebesgue measurable,then a bounded G integrable function is Lebesgue integrable;also we prove that these integrals are equal. |
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| Keywords: | G integrable Lebesgue measurable Lebesgue integrable |
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