中文摘要：

考虑两无穷区间上积分交换次序定理的充分条件,经典定理的充分条件要求函数在二重无界区域上绝对可积,这个条件太强,将经典的二重广义积分的绝对可积条件换成积分的内闭一致收敛性条件,得到数学分析中应有的广泛条件下的两积分交换次序结果。利用广泛条件下的两积分交换次序定理,对广义菲涅尔积分计算中的积分可交换次序给出了一般性证明方法,统一了相关广义积分的计算问题,沟通了不同方法之间的内在联系,给出的方法简单直接。

英文摘要：

Considered the sufficient condition of exchange theorem of integral sequence within two infinite interval,sufficient condition of classical theory is very strong which require function absolutely integrable in twice unbounded intervals. If the absolutely integrable condition of classic twice integral into internal uniform convergence of integral is changed,the result of twice integral exchanging sequence within reasonable generalized condition of mathematical analysis is gained. Used the exchange theorem of integral sequence within the generalized condition,the general proof of integrals exchange of the generalized Fresnel integral which unify the calculation of generalized integrals is given. Furthermore,this method can improve the efficiency of calculation.