Some remarks on the value distribution of meromorphic functions

Abstract

1. Let E be a closed set in the complex plane and f a meromorphic function outside E omitting a set 3. We shall consider the following problem: I f E is thin, under what conditions is F thin, too? In Chapter 2 we consider the case when E and F are of Hausdorff dimension less than one. In Chapter 3 E and F are countable sets with one limit point, and in Chapter 4 E is a countable set whose points converge to infinity, f is entire, and F is allowed to contain at most one finite value.