两无穷区间上广义积分交换次序定理  

Improper Integrals Exchange Theorem on Infinite Interval

作　　者：高建全[1] 邢家省[2] 杨义川[2] GAO Jianquan;XING Jiasheng;YANG Yichuan(Pingdingshan Institute of Education,Pingdingshan 467000,Henan China;Department of Mathematics,LMIB of the Ministry of Education,Beihang University,Beijing 100191,China)

机构地区：[1]平顶山教育学院,河南平顶山467000 [2]北京航空航天大学数学与系统科学学院,数学、信息与行为教育部重点实验室,北京100191

出　　处：《河南科学》2017年第6期845-851,共7页Henan Science

基　　金：国家自然科学基金资助项目(11271040);面向对象的数学公共课实践

摘　　要：考虑两无穷区间上的广义积分交换次序定理的充分条件的问题,指出了经典定理的充分条件过于严格.运用函数列积分极限理论结果,对经典严格的充分条件在表述上给予了改进,从而得到在广泛条件下的广义积分交换次序定理,通过实例说明应用.While the sufficient conditions for improper integrals exchange theorem on infinite interval areusually considered in their practical application,some strict requirements of them are pointed out in this paper.The description of these requirements is improved by the results of the limit theory of function column integrals.The improper integrals exchange theorem with a wide range of conditions is given,and its validity and feasibility isproved by an application example.

关 键 词：无穷区间上的积分交换次序定理 含参变量广义积分 内闭一致收敛性 函数列积分的极限理论 菲涅尔积分 

分 类 号：O177.2[理学—数学]