【摘要】 在本論文中，我們介紹了基于Caratheodory測度理論上的Lebesgue測度理論.從可測集的定義出發(fā)，我們討論可測集的性質(zhì).我們還討論了可測集和Borel集之間的關(guān)系.為了更好地了解可測集的性質(zhì)，我們在文中給出一些例子.通過寫這篇論文，我對可測集的性質(zhì)及其結(jié)構(gòu)有了更深刻全面的了解.

【關(guān)鍵字】測度 可測集 性質(zhì)












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








目錄

1. 引言 1
2. 可測集的定義 2
3. 可測集的性質(zhì) 4
(1)零測集 4
(2)可測集關(guān)于集合的運算性質(zhì) 5
(3)單調(diào)的可測集序列 9
4. 可測集類及可測集的構(gòu)成 11
(1)可測集類 11
(2)可測集與 集的關(guān)系 14
參考文獻(xiàn)、致謝 20