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A proof of the great Picard theorem. (English) Zbl 1069.30047
Great Picard Theorem: If $$z_0$$ is a point of the Riemann sphere $$\mathbb C^*$$ and $$f$$ is a function which is holomorphic in a punctured neighborhood of $$z_0$$ and has an essential singularity at $$z_0$$ then in every neighborhood of $$z_0$$ the function $$f$$ takes every complex value, with at most one exception, infinitely many times.
The author gives a simple and self contained proof of the Great Picard Theorem based on certain Harnack-type inequalities due to J. Lewis.
##### MSC:
 30D20 Entire functions of one complex variable (general theory) 30D45 Normal functions of one complex variable, normal families
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