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