It is certainly possible to treat normal families of analytic functions under the heading of meromorphic functions by considering the convergence only in terms of the spherical metric. We have considered analytic and meromorphic functions separately, in part for the sake of simplicity, partly because this was the approach historically, and partly to illustrate some of the difference between the two classes of functions. Results on normal families of analytic functions pertaining to the so-called “Bloch Principle” have been reserved for Chapter 4.
KeywordsAnalytic Function Compact Subset Meromorphic Function Normal Family Modular Function
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