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\section{Empirical Risk Minimization (ERM) principle consistency}  Denote as $R_{emp}(a_l)=inf_{a \in \Lambda}R_{emp}=inf_{a \in \Lambda}\frac{1}{l}_sum_{i=1}^{l}$  \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}  R(a_l) \xrightarrow[l \rightarrow \infty]{P} \inf_{a \in \Lambda}R(a)