Zalcman's Lemma

Let  be a family of meromorphic functions on the unit disk  which are not normal at 0. Then there exist sequences  in , , , and a nonconstant function  meromorphic in the plane such that

locally and uniformly (in the spherical sense) in the complex plane  (Schwick 2000), where  and .

REFERENCES:

Schwick, W. "A Note on Zalcman's Lemma." New Zealand J. Math. 29, 71-72, 2000.

Zalcman, L. "A Heuristic Principle in Complex Function Theory." Amer. Math. Monthly 82, 813-817, 1975.