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\end{equation}  Then. due to (\ref{eq:strict_consistency})   \begin{equation}  P\bigg\{ \big( P\big\{  \inf_{a \in \Lambda}R_{emp}(a) - \inf_{a \in \Lambda}R_(a)\big)  \geq \frac{\epsilon}{2} \bigg\} \big\}  \xrightarrow[l \rightarrow \infty]{} 0 \end{equation}  and  \begin{equation}  P\bigg\{ \big( \inf_{a P\big\{\inf_{a  \in \Lambda(T+\epsilon)}R_{emp}(a) - \inf_{a \in \Lambda}R_(a)\big)  \geq \frac{\epsilon}{2} \bigg\} \big\}  \xrightarrow[l \rightarrow \infty]{} 1 \end{equation}