deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 93e2ea5..2bc3775 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\begin{equation}  P\bigg\{\sup_{a\in \Lambda} \bigg (\int Q(z,a)dF(z) - \frac{1}{l}\sum_{i=1}^{l}Q(z_i,a) \bigg ) > \epsilon \bigg \} \xrightarrow[l \rightarrow \infty]{} 0,  \end{equation}  for any $\epsilon > 0$, is calledone-sided  uniform one-sided  convergence of means to their mathematical expectations over a given set of functions.   \noindent \textbf{Theorem 1.1} Let there exist the constants $\beta$ and $B$ such that for all functions $Q(z,a)$, $a \in \Lambda$ and for a given distribution $F(z)$ the inequalities   \begin{equation} 
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Then the following two statements are equivalent:  \begin{enumerate}  \item asd For the given distribution function $F(z)$, the ERM principle is strictly consistent on the set of functions $Q(z,a)$, $a \in \Lambda$.  \item 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 $Q(z,a)$, $a \in \Lambda$.  \end{enumerate}