# Iversen theorem

If $a$ is an isolated essential singularity of an analytic function $f(z)$ of a complex variable $z$, then every exceptional value $\alpha$ in the sense of E. Picard is an asymptotic value of $f(z)$ at $a$. For example, the values $\alpha_1=0$ and $\alpha_2=\infty$ are exceptional and asymptotic values of $f(z) = \mathrm{e}^z$ at the essential singularity $a=\infty$. This result of F. Iversen [Iv] supplements the big Picard theorem on the behaviour of an analytic function in a neighbourhood of an essential singularity.
Iversen's theorem has been extended to subharmonic functions on $\R^n$, notably by W.K. Hayman, see [HaKe], [Ha].