Radial and Angular Limits of Meromorphic Functions

Abstract

Let us say that a function denned in the open unit disk D has the Montel property if the set of those points eiθ on the unit circle C where the radial limit exists coincides with the set where the angular limit exists. By a classical theorem of Montel (4), every bounded holomorphic function has this property. Meromorphic functions omitting at least three values and, more generally, the normal functions recently introduced by Lehto and Virtanen (3) also enjoy the Montel property (also see 1).