The Range of an Analytic Function
In this chapter the range of an analytic function is investigated. A generic problem of this type is the following: Let ℱ be a family of analytic functions on a region G which satisfy some property P. What can be said about f(G) for each f in ℱ? Are the sets f(G) uniformly big in some sense? Does there exist a ball B(a; r) such that f(G) ⊃ B(a; r) for each f in ℱ? Needless to say. the answers to such questions depend on the property P that is used to define ℱ.
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