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 $U$. U$ (i.e., bounded and real-valued). Under what conditions does $f$ have a continuous extension to the closure $\overline U$?
|
2 | added the word bounded to clarify, though the image of $f$ was already $[0,1]$ | ||
|
|
||||
|
|
1 |
|
||
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 $\overline U$?
|
||||
