deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 5875f2c..739e2ce 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\begin{equation}  A \triangleq \sup_{a \in \Lambda} \bigg(\int Q(z,a)dF(z) - \frac{1}{l}\sum_{i=1}^{l}Q(z_i,a) \bigg) > \epsilon  \end{equation}  takes place. place and there will be $a^* \in \Lambda$ such that   \begin{equation}  \int Q(z,a^*)dF(z) - \frac{1}{l}\sum_{i=1}^{l}Q(z_i,a^*) > \epsilon  \end{equation}