瑕积分的收敛性与Lebesgue可积性  

The Convergence and Lebesgue Integrability of Defective Integrals

作　　者：梁志刚[1] 曾晓晨 LIANG Zhigang;ZENG Xiaochen(Department of Mathematics,Faculty of Science,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学理学部数学系,北京100124

出　　处：《大学数学》2023年第1期72-78,共7页College Mathematics

基　　金：国家自然科学基金(11901019);北京市教委科研计划资助(KM202010005025);北京工业大学教育教学研究课题资助(ER2020B070)。

摘　　要：瑕积分的收敛性与Lebesgue可积性之间具有密不可分的关系.首先详细证明了瑕积分收敛定理,然后说明无穷积分的收敛定理与瑕积分的收敛定理是等价的,最后利用两条定理的等价性给出一个应用.This paper discusses the relation between the convergence and Lebesgue integrability of defective integrals.The convergence theorem of defective integrals is proved in detail.Then we show that the convergence theorem of infinite integrals is equivalent to that of defective integrals.Finally,an application is given by using the equivalence of two theorems.

关 键 词：瑕积分 无穷积分 RIEMANN积分 LEBESGUE积分 

分 类 号：O174.1[理学—数学]