Question: Let f be a convex function on an open set S that is bounded at a single point. Show that f is locally bounded, that

Let f be a convex function on an open set S that is bounded at a single point. Show that f is locally bounded, that is for every x ∈ S there exists a constant M and neighborhood U containing x such that
|f(x′)| ≤ M for every x′ ∈ U

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