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\end{equation}  for any $\epsilon > 0$, is called uniform one-sided convergence of means to their mathematical expectations over a given set of functions.    \noindent \textbf{Theorem 1.1} 1.1 (Key Theorem).}  \textit{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}  \beta \leq \int Q(z,a)dF(z) \leq B , \:\: a \in \Lambda  \end{equation}