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\end{equation}  \textit{are valid.   Then the following two statements are equivalent: equivalent:}  \begin{enumerate}  \item For \textit{For  the given distribution function $F(z)$, the ERM principle is strictly consistent on the set of functions $Q(z,a)$, $a \in \Lambda$. \Lambda$.}  \item For \textit{For  the given distribution function $f(z)$, the uniform one-sided convergence of the means to their mathematical expectations takes place over the set of functions $Q(z,a)$, $a \in \Lambda$. } \Lambda$.}  \end{enumerate}