函数列一致收敛的一个充要条件

A Necessary and Sufficient Condition for Uniform Convergence of Function Sequence

一致收敛的判别法对于函数列分析性质非常重要,Dini判别法是常见的判别方法,但它要求的条件相当强,不具普遍性.文章从点列角度出发给出函数列一致收敛的一个充要条件,并举例阐述其对判断是否一致收敛的有效性.

The uniform convergence criterion for the analysis of the nature of function sequence is very important, Dini discrimination is a common law judge, but it requires a very strong condition,and is not universal. A necessary and sufficient condition to the uniform convergence of function sequence is provided in this article from the point of view,and this article sets some examples to determine whether the uniform convergence has the same effectiveness.