deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 1918155..b085d1c 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\end{equation}  We denote as $T_k$ the event   \begin{equation}  \label{eq:cons_eventTk}  \inf_{a \in \Lambda(\beta_k)} \int Q(z,a)dF(z) - \inf_{a \in \Lambda(\beta_k)} \frac{1}{l} \sum_{i=1}^{l} Q(z_i,a) > \frac{\epsilon}{2}  \end{equation}  and as $T$ the event $\cup_{k=1}^nT_k$. Then by virtue of (\ref{eq:cons_in_prob})  
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\end{equation}  For the chosen set $\Lambda(\beta_k)$ the inequality  \begin{equation}  \label{eq:cons_eventA}  \int Q(z,a^*)dF(z) - \inf_{a \in \Lambda(\beta_k)} \int Q(z,a)dF(z) < \frac{\epsilon}{2}  \end{equation}  is valid. Using (\ref{eq:cons_eventTk}) and (\ref{eq:cons_eventA}) the inequalities   \begin{equation}  \label{eq:cons_AleqTk}  \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^*) + \espilon > \inf_{a \in \Lambda(\beta_k)} \frac{1}{l} \sum_{i=1}^{l} Q(z_i, a) + \epsilon  \end{equation}