(R)可积函数列逐项积分的充要条件

Necessary and sufficient conditions of term by term Integrability of sequence of(R) integrable functions

通过对点态收敛(R)可积函数列积分运算与极限运算可交换条件的讨论,引进了弱一致(R)可积的概念,从而给出了闭区间上(R)可积函数列积分运算与极限运算可交换的充要条件.

The concept of weak uniform （R） integrability was introduced by means of integral operation of point-convergent （R） integrable functional sequence and by discussing exchangeable condition of limiting operation, so that the necessary and sufficient condition of term by term integrability of sequence of （R） integrable functions on closed interval was given.