瑕积分的收敛性与Lebesgue可积性

The Convergence and Lebesgue Integrability of Defective Integrals

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.