deletions | additions       diff --git a/untitled.tex b/untitled.tex  index acfa759..b6abf05 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\inf_{a \in \Lambda(\beta_k)} \int Q(z,a)dF(z) + \frac{\epsilon}{2} & > \int Q(z,a^*)dF(z) \\ > \frac{1}{l}\sum_{i=1}^{l}Q(z_i. a^*) + \epsilon & > \inf_{a \in \Lambda(\beta_k)} \frac{1}{l} \sum_{i=1}^{l} Q(z_i, a) + \epsilon  \end{split}  \end{equation}  hold and implie that event $T_k$ aldo also  takes place. This means that \begin{equation}  A \subseteq T_k \subseteq T \Longrightarrow P(A) \leq P(T_k) \leq P(T) \xrightarrow[l \rightarrow \infty]{} 0 .  \end{equation}