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We denote as $T_k$ the event   \begin{equation}  \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 $\cup_{k=1}^nT_k$