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is the union of events  \begin{equation}  A_1 \triangleq \inf_{a \in \Lambda(c)} \int Q(z,a)dF(z) + \epsilon < \inf_{a \in \Lambda(c)} \frac{1}{l} \sum_{i=1}^{l}Q(z_i,a)  \end{equation}  and  \begin{equation}  A_2 \triangleq \inf_{a \in \Lambda(c)} \int Q(z,a)dF(z) - \epsilon > \inf_{a \in \Lambda(c)} \frac{1}{l} \sum_{i=1}^{l}Q(z_i,a)  \end{equation}