View source for Iversen theorem

{{MSC|32H25}}
{{TEX|done}}

If $a$ is an isolated essential singularity of an analytic function $f(z)$ of a complex variable $z$, then every [[Exceptional     value|exceptional value]] $\alpha$ in the sense of E. Picard is an [[Asymptotic value|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 {{Cite|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 {{Cite|HaKe}}, {{Cite|Ha}}.

====References==== 
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|valign="top"|{{Ref|CoLo}}||valign="top"| E.F. Collingwood, A.J. Lohwater, "The theory of cluster sets", Cambridge Univ. Press (1966) pp. Chapt.  1;6
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|valign="top"|{{Ref|Ha}}||valign="top"| W.K. Hayman, "Subharmonic functions", '''2''', Acad. Press (1989)
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|valign="top"|{{Ref|HaKe}}||valign="top"| W.K. Hayman, P.B. Kennedy, "Subharmonic functions", '''1''', Acad. Press (1976)
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|valign="top"|{{Ref|Iv}}||valign="top"| F. Iversen, "Récherches sur les fonctions inverses des fonctions méromorphes", Helsinki (1914)
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