On the Metrical Theorems of Cluster Sets of Meromorphic Functions

Abstract

Recently the important contributions to the cluster sets theory of the meromorphic functions in the unit-disc have been done by many authors. For its recent development, we refer to K. Noshiro [10]. Roughly speaking, these studies can be divided into two classes ; the first one is topological, and the second one is metrical. As far as the author knows, there exist very few results on the metrical theorems on cluster sets of functions meromophic in an arbitrary connected domain, except for the case that its boundary is of logarithmic capacity zero. (K. Noshiro [10] pp. 5-31).