deletions | additions       diff --git a/section_Convergence_label_sec_convergence__.tex b/section_Convergence_label_sec_convergence__.tex  index 5963282..495357f 100644  --- a/section_Convergence_label_sec_convergence__.tex  +++ b/section_Convergence_label_sec_convergence__.tex 
...
%But it is also interesting to characterize the class of opinion profiles on which \emph{any} influence graph would make the resulting opinion stream converge:  \begin{lemma}\label{lemma:opinion}  Let $\G$ be an influence profile and $\O=(O_1,\dots,O_n)$ $\O$  be an opinion profile. Then the following are equivalent: \begin{itemize}  \item[] The BDP converges for $\O$ on $\G$.  \item[] For all $p\in \Atoms$, there is no set of agents $C\subseteq\N$ such that: $C$ is a cycle in $G_{p}$ and there are two agents $i,j\in C$ such that $O_i(p)\neq O_j(p)$. 
...
Combining the above results we obtain:  \begin{theorem} \label{theorem:convergence}  Let $\G$ be an influence profile and $\O=(O_1,\dots,O_n)$ $\O$  be an opinion profile. The BDP converges for $\O$ on $\G$ if and only if: \begin{itemize}  \item[] For all $p\in\Atoms$, $G_p$ contains no cycle of length $\geq 2$, or  \item[] For some $p\in\Atoms$, there is a set of agents $C\subseteq\N$ such that: $C$ is a cycle in $G_{p}$ and there are two agents $i,j\in C$ such that $O_i(p)\neq O_j(p)$.