AENC/resampling_chain Changeset - 231f5e366818 · Centrum Wiskunde & Informatica (CWI)

Changeset - 231f5e366818

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András Gilyén - 8 years ago 2017-09-06 15:22:19
gilyenandras@gmail.com

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     \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.

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