关于R可积函数空间的完备化  

On the Completion of the Riemann Product Function Space

作　　者：李忠宁[1] 

机构地区：[1]银川大学基础部数学教研组,宁夏银川750105

出　　处：《河西学院学报》2010年第5期14-18,共5页Journal of Hexi University

摘　　要：完备性是度量空间中的一个重要性质,本文运用了实变函数中点集分析的方法及其相关定义和定理讨论了Riemann积分与Lebesgue积分的本质区别在于:R[a,b]作为L[a,b]的子空间是不完备的,而L[a,b]是完备的,并证明了R[a,b]在L[a,b]中稠密,最后得到了L[a,b]是R[a,b]的完备化空间.Completeness is an important property in the metric space.In this paper,the essential difference between R [a, b] integration and L [a, b] integration is discussed with the method of point set-analysis and related defines and theories in Real Function.The difference is that R [a, b] as the subspace of L [a, b] is incomplete and L [a, b] is complete.It also proves that R [a, b] is dense in L [a, b].Finally,it obtains that L [a, b] is the completion space of R [a, b].

关 键 词：R[a b] L[a b] 完备 稠密 完备化空间 

分 类 号：O174.1[理学—数学]