diff --git a/src/fa/convex/legendre.tex b/src/fa/convex/legendre.tex
index 544595f..6cd6a79 100644
--- a/src/fa/convex/legendre.tex
+++ b/src/fa/convex/legendre.tex
@@ -195,7 +195,7 @@
 
     Since for any $(y, \beta) \in A$, $\beta$ may be arbitrarily large by \autoref{lemma:closed-convex-epigraph}, $\mu \le 0$. 
 
-    In the case that $\mu < 0$, for each $y \in E$, 
+    In the case that $\mu < 0$, for each $y \in \bracs{f < \infty}$, 
     \begin{align*}
         \dpn{x, \phi}{\lambda} + \mu\alpha &> \dpn{y, \phi}{\lambda} + \mu f(y) \\
         \dpn{x, \mu^{-1}\phi}{\lambda} + \alpha & < \dpn{y, \mu^{-1}\phi}{\lambda} + f(y) \\