On a problem of Lohwater about the asymptotic behaviour in Nevanlinna’s class

Abstract:

Let $f(z)$ be meromorphic in $|z| < 1$ and let the radial limits ${\lim _{r \to 1}}f(r{e^{i\theta }})$ exist and have modulus 1 for almost all $e^{i\theta } \in A = \{ e^{i\theta }: \theta _1 \leqslant \theta \leqslant \theta _2 \}$. If $P$ is a singular point of $f(z)$ on $A$, then every value of modulus 1 which is not in the range of $f(z)$ at $P$ is an asymptotic value of $f(z)$ at some point of each subarc of $A$ containing the point $P$. This answers in the affirmative sense a question of A. J. Lohwater.