diff --git a/src/fa/convex/legendre.tex b/src/fa/convex/legendre.tex index 2f9a60c..fa9b0e2 100644 --- a/src/fa/convex/legendre.tex +++ b/src/fa/convex/legendre.tex @@ -150,7 +150,7 @@ f^{**}(x) = \sup\bracs{\dpn{x, \phi}{\lambda} - \alpha|(\phi, \alpha) \in F \times \real, (\phi, \alpha) \le f} \] \item $\text{epi}(f^{**})$ is the $\sigma(E \times \real, F \times \real)$-closed convex hull of $\text{epi}(f)$. - \item The biconjugate $f^{**}$ is the greatest convex and $\sigma(E, F)$-lower semicontinuous function bounded above by $f$. + \item $f^{**}$ is the greatest convex and $\sigma(E, F)$-lower semicontinuous function bounded above by $f$. \item $f = f^{**}$ if and only if $f$ is convex and $\sigma(E, F)$-lower semicontinuous. \end{enumerate} \end{theorem}