Applicating integrable functions using the integral supremum method, this paper gives a sufficient and necessary condition to conclude the degree sequence of functions with absolutely continuous integration, it also gives sequence of functions with absolutely continuous degree of integration such as a series of equivalent propositions, in order to improve the integration and limit the exchange order.%应用对可积函数列取积分上确界方法，给出函数列具有积分等度绝对连续的一个充要条件，得出函数列具有积分等度绝对连续的一系列等价命题，从而完善了积分和极限交换顺序．
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