论文1康托尔和集合论.docVIP

 PAGE \* MERGEFORMAT i 目录 TOC \o 1-5 \h \u  HYPERLINK \l _Toc26626 1引言  PAGEREF _Toc26626 1  HYPERLINK \l _Toc2502 2康托集和集合论  PAGEREF _Toc2502 1  HYPERLINK \l _Toc13585 2.1集合论与测度的几个定义定理  PAGEREF _Toc13585 1  HYPERLINK \l _Toc2200 2.1.1集类的相关定义  PAGEREF _Toc2200 1  HYPERLINK \l _Toc14397 2.1.2单调函数与测度的构造的相关定义定理  PAGEREF _Toc14397 4  HYPERLINK \l _Toc27477 2.1.3可测函数与分布的相关定  PAGEREF _Toc27477 5  HYPERLINK \l _Toc2537 2.2集合论的建立  PAGEREF _Toc2537 7  HYPERLINK \l _Toc19656 2.2.1康托集的建立  PAGEREF _Toc19656 7  HYPERLINK \l _Toc5572 2.2.2康托尔集的性质  PAGEREF _Toc5572 10  HYPERLINK \l _Toc32178 2.3零测集和离散型随机变量的联系  PAGEREF _Toc32178 11  HYPERLINK \l _Toc22069 3结论  PAGEREF _Toc22069 12  HYPERLINK \l _Toc20730 4结束语  PAGEREF _Toc20730 12  HYPERLINK \l _Toc29745 参考文献  PAGEREF _Toc29745 13  HYPERLINK \l _Toc11940 致谢  PAGEREF _Toc11940 14   PAGE \* MERGEFORMAT ii 集合论与测度 数学系本0903班 黄丽芳 指导教师：陈金梅 摘 要：本文首先介绍了集合论中的一种特殊的集合——康托尔集，接着以零测集和可测函数为内容将概率空间和测度空间做了相应的联系，将概率论的相关知识与实变函数的相关知识做了很好的衔接。测度论是概率理论的必要基础，对比学习测度和分布变量为以后概率和统计专业知识的学习做了很好的旧知识的复习和新知识基础的巩固。文章给出的相关定义和定理为论文的知识提供了很好的理论依据。通过该论文的写作，不仅将此阶段前的集合基础知识做了复习，还对以后进一步的学习做了必要的准备。 关键词：集合论，测度论，学习，分布变量，可测函数。 Set theory and measurement Huang Lifang The Mathematics Department of 0903 class Tutor : Chen Jinmei Abstract:At first,this paper introduces a special set -- Cantor set theory of set. After that ,I choose the zero measure set and measurable function form the content of probability space and measure space.It is easy to connect the knowledge of probability theory with the real variable function . Measure theory is based on probability theory, and in turn reviewing the measure and the variables. It is necessary for this paper to provide a good theoretical basis related definitions and theorems . Through this paper , I review the set of knowledge prior to this stage.This paper will be able to play the very big imputes role to my further study. Keywords: set theo