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?
Is a convex function defined on a convex open subset of $\mathbb R^n$ continuous?
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real-analysis
convex-analysis
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0@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