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\label{eq:cons_prob_0}  P\bigg\{\inf_{a \in \Lambda(T+\epsilon)}R_{emp}(a) - \inf_{a \in \Lambda}R(a) \geq \frac{\epsilon}{2} \bigg\} \xrightarrow[l \rightarrow \infty]{} 1  \end{equation}  are valid for any $\epsilon > 0$. (\ref{eq:cons_prob_1}) and (\ref{eq:cons_prob_0}) imply that $a_l \notin \Lambda(T+\epsilon)$ \Lambda(T+\epsilon)$. Thus, form the definition of subsets $\Lambda(c)$ the following inequalities  \begin{equation}  T \geq \int Q(z,a_l) df(z) \geq T+\epsilon  \end{equation}  hold. \Box