X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rairo15.git/blobdiff_plain/3820ec6286eab552baad3b3d7c0451e1bbc42482..039eee12186be85d7a74a188489abd12bfe554fd:/stopping.tex?ds=inline

diff --git a/stopping.tex b/stopping.tex
index 567ab01..d095a3a 100644
--- a/stopping.tex
+++ b/stopping.tex
@@ -176,14 +176,16 @@ let $S_{X,\ell}$ be the
 random variable that counts the number of steps 
 from $X$ until we reach a configuration where
 $\ell$ is fair. More formally
-$$S_{X,\ell}=\min \{t \geq 1\mid h(X_{t-1})\neq \ell\text{ and }Z_t=(\ell,\.)\text{ and } X_0=X\}.$$
+$$S_{X,\ell}=\min \{t \geq 1\mid h(X_{t-1})\neq \ell\text{ and }Z_t=(\ell,.)\text{ and } X_0=X\}.$$
 
  We denote by
 $$\lambda_h=\max_{X,\ell} S_{X,\ell}.$$
 
 
 \begin{Lemma}\label{prop:lambda}
-If $\ov{h}$ is a square-free bijective function, then one has $E[\lambda_h]\leq 8n^2.$
+If $\ov{h}$ is a square-free bijective function, then the inequality 
+$E[\lambda_h]\leq 8n^2$ is established.
+
 \end{Lemma}
 
 \begin{proof}
@@ -244,4 +246,4 @@ Theorem~\ref{prop:stop} is a direct application of
 lemma~\ref{prop:lambda} and~\ref{lm:stopprime}.
 \end{proof}
 
-\end{document}
+