黎曼积分的局限性和勒贝格积分的优越性  

On The Shortcomings of Riemann Integral and Advantages of Lebesgue Integral

作　　者：刘松[1] 

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《合肥学院学报（综合版）》2016年第4期14-16,34,共4页Journal of Hefei University：Comprehensive ED

基　　金：安徽大学青年骨干教师培养项目(023033010264)资助

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,Lebesgue积分不仅蕴含了Riemann积分所达到的成果,而且还在较大程度克服了Riemann积分的局限性。从可积函数的连续性,积分极限定理,可积函数空间的完备性和微积分基本定理等方面详细阐述了黎曼积分的局限性和勒贝格积分的优越性。Riemann integral and Lebesgue integral are the key content of Mathematical Analysis and Real Functions, respectively. Lebesgue integral not only contains the achievements of Riemann integral, but also overcomes the drawbacks of Riemann integral in a large extent. This paper mainly intro- duces the shortcomings of Riemann integral and advantages of Lebesgue integral from the aspects of the continuity of integrable functions, integral limitation theorems, completeness of the space of integrable functions and fundamental theorem of calculus

关 键 词：黎曼积分 勒贝格积分 可测函数 

分 类 号：O171[理学—数学]