关于Riemann积分理论的本质缺陷及以Lebesgue积分理论取代之的看法  

On the Essential Shortage of the Integral Theory of Riemann and the Opinion to Replace It by the Theory of Lebesgue

作　　者：王昆扬[1] 

机构地区：[1]北京师范大学数学系,100875

出　　处：《数学教育学报》1999年第3期95-98,共4页Journal of Mathematics Education

基　　金：教育部资助的教学改革研究项目

摘　　要：简要论述了Ｒｉｅｍａｎｎ 积分理论的本质缺陷是不承认σ＿ 可加性，而Ｌｅｂｅｓｇｕｅ 积分理论的出发点是σ＿ 可加性，在大学数学系本科基础课中以Ｌｅｂｅｓｇｕｅ 积分取代ＲｉｅｍａｎｎIt was shown briefly that essential shortage of the integral theory of Riemann was to deny σ _additibity which was the starting point of the theory of Lebesgue; the replacement of Riemann's theory by Lebesgue's in the basic courses of the mathematical department of universities must be historically necessary.

关 键 词：RIEMANN积分 LEBESGUE积分 缺陷 积分理论 

分 类 号：O172.2[理学—数学]