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added the word bounded to clarify, though the image of $f$ was already $[0,1]$
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Tom LaGatta
Tom LaGatta
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Let $U$ be an open convex set in a locally convex space $X$, and let $f : U \to [0,1]$ be a real-valued log-concave function on $U$ (i.e., bounded and real-valued). Under what conditions does $f$ have a continuous extension to the closure $\overline U$?

Let $U$ be an open convex set in a locally convex space $X$, and let $f : U \to [0,1]$ be a real-valued log-concave function on $U$. Under what conditions does $f$ have a continuous extension to the closure $\overline U$?

Let $U$ be an open convex set in a locally convex space $X$, and let $f : U \to [0,1]$ be a log-concave function on $U$ (i.e., bounded and real-valued). Under what conditions does $f$ have a continuous extension to the closure $\overline U$?

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Tom LaGatta
Tom LaGatta
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Does a log-concave function on a convex set extend continuously to the boundary?

Let $U$ be an open convex set in a locally convex space $X$, and let $f : U \to [0,1]$ be a real-valued log-concave function on $U$. Under what conditions does $f$ have a continuous extension to the closure $\overline U$?