关于Arzela定理的条件的减弱

A Reduction of the Condition On Arzela's Theorem

证明了在Arzela定理中 ,将函数列 (fn) ∞n =1在一闭的有界区间 [a ,b]上一致有界减弱为“弱一致有界”时 。

Let (f n) ∞ n=1 be a sequence of function on the bounded closed interval ,We proved that the conclusion of Arzela's Theorem is also true if (f n) ∞ n=1 is weakly uniformly bounded and not uniformly bounded on .\;