From 231f5e36681842e966fb1f869fa2b3b31739bec2 2017-09-06 15:22:19
From: András Gilyén <gilyenandras@gmail.com>
Date: 2017-09-06 15:22:19
Subject: [PATCH] Update on Overleaf.
---

diff --git a/main.tex b/main.tex
index 2c1d611a06586de104dbf85fd91e513423ea577b..90cd09fe22be9c748fb4eeaf9dfa30c7beed2255 100644
--- a/main.tex
+++ b/main.tex
@@ -887,10 +887,10 @@ Note by Tom: So $A^{(\mathcal{P})}$ is the event that the set of all patches is
     \end{itemize} 
     
 	\begin{lemma}On the infinite chain
-		$$\P_I(Z^{0}\cap Z^{k})=\P_I(Z^{0})\P_I(Z^{k})+\mathcal{O}(p^{k-|b|+1})$$
+		$$\P_I(Z^{0}\cap Z^{k})=\P_I(Z^{0})\P_I(Z^{k})+\mathcal{O}(p^{k-|I|+1})$$
 	\end{lemma}   
     Note that using De Morgan's law and the inclusion-exclusion formula we can see that this is equivalent to saying:
-    $$\P_I(NZ^{0}\cap NZ^{k})=\P_I(NZ^{0})\P_I(NZ^{k})+\mathcal{O}(p^{k-|b|+1})$$
+    $$\P_I(NZ^{0}\cap NZ^{k})=\P_I(NZ^{0})\P_I(NZ^{k})+\mathcal{O}(p^{k-|I|+1})$$
     \begin{proof}
     We proceed by induction on $|I|$. For $|I|=0,1$ the statement is trivial.