设F为区域D内的一族亚纯函数, 对于每个f∈F, f的所有极点重数至少是2, a(z)和b(z)为两个在D内满足 的全纯函数. 若对于每个f∈F,f(z)≠a(z)和f(z)≠b(z), 则F 在D内正规.这个结果改进了经典的Montel定则. 此外,我们也讨论了亚纯函数族中每个函数与其导函数分担两个全纯函数的正规性.  

Let F be a family of meromorphic functions in a domain D, all of whose poles are multiple. Let a(z) and b(z) be holomorphic functions in D such that . If, for every f ∈F, f(z)≠ a(z) and f(z)≠ b(z), then F is normal in D. This improves the classic Montel's normality criterion. Moreover, we discuss the normality of families of meromorphic functions in which every function shares two holomorphic functions with its derivative.