We show that a family of functions meromorphic in a plane domain D whose spherical derivatives are uniformly bounded away from zero is normal. Furthermore, we show that for each f meromorphic in the unit disk D, infz∈Df#(z) ≤ 1/2, where f# denotes the spherical derivative of f.
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∗Part of this work was supported by the German Israeli Foundation for Scientific Research and Development (No. G 809−234.6/2003). Shahar Nevo also received support from the Israel Science Foundation, Grant No. 395/07. This research is part of the European Science Foundation Networking Programme HCAA.