如极限收敛，停时定理等很多方面都与一致可积性有着重要联系。
There are many results with important relations to it , such as the covergance theorem and stopping time .
本文给出了非一致收敛的几个定理 ，并以较多的实例说明它们的应用。
Several theorems about non-uniform convergence and a few examples were used to explain the application of them.
最后证明基于双重随机样本的统计学习理论的关键定理并讨论学习过程一致收敛速度的界。
Finally the key theorem of statistical learning theory based on random rough samples is proved, and the bounds on the rate of uniform convergence of learning process are discussed.
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