diff --git a/src/fa/convex/legendre.tex b/src/fa/convex/legendre.tex
index f10889d..5f1a7de 100644
--- a/src/fa/convex/legendre.tex
+++ b/src/fa/convex/legendre.tex
@@ -269,7 +269,7 @@
 
 \begin{corollary}
 \label{corollary:separable-legendre}
-    Let $\dpn{E, F}{\lambda}$ be a duality over $\real$ and $f: E \to (-\infty, \infty]$ with $f \ne \infty$ be convex and lower semicontinuous, then there exists $\seq{(\phi_n, \alpha_n)} \subset F \times \real$ such that for each $x \in E$, 
+    Let $\dpn{E, F}{\lambda}$ be a duality over $\real$ with $E$ being separable, and $f: E \to (-\infty, \infty]$ with $f \ne \infty$ be convex and lower semicontinuous, then there exists $\seq{(\phi_n, \alpha_n)} \subset F \times \real$ such that for each $x \in E$, 
     \[
     f(x) = \sup_{n \in \natp} \dpn{x, \phi_n}{\lambda} - \alpha_n
     \]