From 67b00db2761dbc1c16250e26a0b4679d30f4958d Mon Sep 17 00:00:00 2001 From: Bokuan Li Date: Thu, 9 Jul 2026 12:47:54 -0400 Subject: [PATCH] Fix typo. --- src/fa/lc/hahn-banach.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/fa/lc/hahn-banach.tex b/src/fa/lc/hahn-banach.tex index afa9941..8440429 100644 --- a/src/fa/lc/hahn-banach.tex +++ b/src/fa/lc/hahn-banach.tex @@ -26,10 +26,10 @@ then for any $x \in F$ and $t > 0$, \begin{align*} - \phi(x + tx_0) &= \phi(x) + t\lambda = t\braks{\phi(t^{-1}x) + \lambda} \\ + \phi_{x_0, \lambda}(x + tx_0) &= \phi(x) + t\lambda = t\braks{\phi(t^{-1}x) + \lambda} \\ &\le t\braks{\rho(t^{-1}x + x_0) - \phi(t^{-1}x) + \phi(t^{-1}x)} \\ &= t\rho(t^{-1}x + x_0) = \rho(x + tx_0) \\ - \phi(x - tx_0) &= \phi(x) - t\lambda = t\braks{\phi(t^{-1}x) - \lambda} \\ + \phi_{x_0, \lambda}(x - tx_0) &= \phi(x) - t\lambda = t\braks{\phi(t^{-1}x) - \lambda} \\ &\ge t\braks{\rho(t^{-1}x - x_0) + \phi(t^{-1}x) - \phi(t^{-1}x)} \\ &= t\rho(t^{-1}x - x_0) = \rho(x - tx_0) \end{align*}