一个新的正规定则

A new normal criterion

证明了单位圆内亚纯函数族F,若不正规,则存在一个函数列在开平面上的任意紧子集上一致收敛于一个非常数的亚纯函数,并应用它得到一个新的正规定则:设F为区域D内的一亚纯函数族,若对每一f∈F,fnf′≠1(n2),则F在区域D内正规。

If a family of meromorphic functions is not normal in the unit disk then there exists a series of functions which converge to a non-constant meromorphic function uniformly in any compact set in the open plane. It is used to prove a new normal criterion: a family of meromorphic functions in a domain D satisfying that fnf′≠1 has no zero is a normal one.