黎曼积分与勒贝格积分的区别与联系摘 要：黎曼积分和勒贝格积分分别是数学分析及实变函数的核心内容。本文从学过的黎曼积分和勒贝格积分的知识出发，探讨和归纳出两者之间的区别与联系。从积分的定义，积分的存在条件，积分的性质，可积函数类，积分相关定理五个方面阐述了黎曼积分与勒贝格积分的区别。通过对勒贝格积分与黎曼积分发展过程的分析与探讨归纳出二者的区别与联系。关键词：黎曼积分；勒贝格积分；区别；联系。Abstract：Riemann integral and the Lebesgue integral which is the core content of mathematical analysis and the real variable function. This paper studied the Riemann integral and the Lebesgue integral knowledge of, and discusses the difference and connection between the two. From the definition of integral, the continuity of integrable function, the additivity of integral, integral limit theorem, five aspects of Newton - Leibniz formula describes the distinctions between Riemann integral and Lebesgue integral. Through the analysis and Discussion on the Lebesgue integral and the Riemann integral development process induces the difference and connection between the two.Keyword：Riemann integral；Lebesgue integral；difference；relationship目录1 引言.............................................................................................................................31.1 微积分的发展史..............................................................................................31.2 黎曼积分与勒贝格积分的引入......................................................................32 黎曼积分与勒贝格积分的定义.................................................................................52.1 黎曼积分的定义..............................................................................................52.2 勒贝格积分的定义..........................................................................................62.3 黎曼积分和勒贝格积分定义区别与联系.................................
