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Denote as   \begin{equation}  R_{emp}(a_l) \triangleq \inf_{a \in \Lambda}R_{emp}=\inf_{a \Lambda}R_{emp}(a_l)=\inf_{a  \in \Lambda}\frac{1}{l}\sum_{i=1}^{l}Q(z_i,a) \end{equation}  \textbf{Definition.} ERM principle is \textit{consistent} for the set of functions $Q(z,a)$, $a \in \Lambda$ and the probability distribution $F(z)$ if the following two sequences converge in probability:  \begin{equation}