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Let $K$ be a convex open set in $\mathbb R^n$ and $f$ a convex function defined on $K$; how to show that $f$ is continuous?

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    @Jeff: See e.g. Theorem 3.3.1 in [these notes](http://ljk.imag.fr/membres/Anatoli.Iouditski/cours/convex/chapitre_3.pdf)2012-11-29

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