| 与康托集有关的一些函数的勒贝格积分 |
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| 引用本文： | 周其生.与康托集有关的一些函数的勒贝格积分[J].安庆师范学院学报(自然科学版),2014(4):1-5. |
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| 作者姓名： | 周其生 |
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| 作者单位： | 安庆师范学院数学与计算科学学院,安徽安庆,246133 |
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| 基金项目： | 安徽省质量工程项目(2012gxko75)省级精品资源共享课程《实变函数》资助。 |
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| 摘 要： | 对一些与康托集有关的函数的勒贝格积分的计算做了讨论，利用学生对康托集构造的兴趣，对一些函数的黎曼可积性和勒贝格可积性作出判定，并利用两种积分的关系计算这些积分，从而加深对勒贝格积分理论的理解。
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| 关 键 词： | 实变函数 康托集 黎曼积分 勒贝格积分 |
The Lebesgue Integral of Some Function Associated with the Cantor Set |
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| ZHOU Qi-sheng.The Lebesgue Integral of Some Function Associated with the Cantor Set[J].Journal of Anqing Teachers College(Natural Science Edition),2014(4):1-5. |
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| Authors: | ZHOU Qi-sheng |
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| Institution: | ZHOU Qi-sheng ( School of Mathematics and Computation Science, Anqing Teachers College, Anqing 246133, China) |
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| Abstract: | Calculation of Lebesgue integral for some function related to the Cantor set is discussed .Using the students＆#39;interest in the structure of the Cantor set, integrability determination is made on some function for Riemann integral and Lebesgue integral , and the relationship between the two kinds of integral is used to calculate these integrals , which deepens the understanding of the theory of the Lebesgue integral. |
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| Keywords: | real variable function Cantor set Riemann integral Lebesgue integral |
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