A Criterion for Normalcy

Paul Gauthier
1968 Nagoya mathematical journal  
Gavrilov [2] has shown that a holomorphic functionf(z) in the unit disc |z|<1 is normal, in the sense of Lehto and Virtanen [5, p. 86], if and only iff(z) does not possess a sequence ofρ-points in the sense of Lange [4]. Gavrilov has also obtained an analagous result for meromorphic functions by introducing the property that a meromorphic function in the unit disc have a sequence of P-points. He has shown that a meromorphic function in the unit disc is normal if and only if it does not possess a sequence ofP-points.
doi:10.1017/s0027763000026702 fatcat:5oir3en3hbajpcg64be3vx7phe