毕业论文 可测集的判定方法及其性质.doc
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毕业论文 可测集的判定方法及其性质,【摘要】 在本论文中，我们介绍了基于caratheodory测度理论上的lebesgue测度理论.从可测集的定义出发，我们讨论可测集的性质.我们还讨论了可测集和borel集之间的关系.为了更好地了解可测集的性质，我们在文中给出一些例子.通过写这篇论文，我对可测集的性质及其结构有了更深刻全面的了解.【关键字】测度可测集性...
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【摘要】 在本论文中，我们介绍了基于Caratheodory测度理论上的Lebesgue测度理论.从可测集的定义出发，我们讨论可测集的性质.我们还讨论了可测集和Borel集之间的关系.为了更好地了解可测集的性质，我们在文中给出一些例子.通过写这篇论文，我对可测集的性质及其结构有了更深刻全面的了解.
【关键字】测度 可测集 性质
Determination Methods and Properties of the Measurable Set
[Abstract] In this paper, we introduce the Lebesgue measure theory which is based on the Caratheodory measure theory. From the definitions of measurable set, we discuss the properties of measurable set. We also discuss the relationship between measurable set and Borel set. In order to obtain a good understanding the properties of measurable set, we give some examples in the paper. Through writing this paper, I get a comprehensive and profound understanding about the construction and properties of measurable set.
[Keywords] Measure Measurable set Properties
目录
1. 引言 1
2. 可测集的定义 2
3. 可测集的性质 4
(1)零测集 4
(2)可测集关于集合的运算性质 5
(3)单调的可测集序列 9
4. 可测集类及可测集的构成 11
(1)可测集类 11
(2)可测集与 集的关系 14
参考文献、致谢 20
【关键字】测度 可测集 性质
Determination Methods and Properties of the Measurable Set
[Abstract] In this paper, we introduce the Lebesgue measure theory which is based on the Caratheodory measure theory. From the definitions of measurable set, we discuss the properties of measurable set. We also discuss the relationship between measurable set and Borel set. In order to obtain a good understanding the properties of measurable set, we give some examples in the paper. Through writing this paper, I get a comprehensive and profound understanding about the construction and properties of measurable set.
[Keywords] Measure Measurable set Properties
目录
1. 引言 1
2. 可测集的定义 2
3. 可测集的性质 4
(1)零测集 4
(2)可测集关于集合的运算性质 5
(3)单调的可测集序列 9
4. 可测集类及可测集的构成 11
(1)可测集类 11
(2)可测集与 集的关系 14
参考文献、致谢 20
