与分担值相关的正规族

Normal Families Related to Shared Values

设F是区域D上的一族亚纯函数,a,b,c是有穷复数,a≠b,c≠0.本文证明:如果对任意的f∈F,f的零点重级至少是k,并且这里我们记(?)Ef（a）={z∈D:f（z）=a},则F在D上正规.同时我们将举例说明对f的零点重级条件的限制是必要的.

Let F be a family of meromorphic functions on a domain D and a, b, c be finite complex values, a≠6, c≠0. It is proved that F is a normal family, provided that for each f ?F, all zeros of f are of multiplicity at least k, andwhere we write . At the same time we show that the condition on multiple zeros of f is necessary.