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\end{equation}  for any $\epsilon > 0$, is called one-sided uniform convergence of means to their mathematical expectations over a given set of functions.    \noindent \textbf{Theorem 1.1} Let there exist the constants $\alpha$ $\beta$  and $\Alpha$ $B$  such that for all functions $Q(z,a)$, $a \in \Lambda$ and for a given distribution $F(z)$ the inequalities \begin{equation}  \alpha \beta  \leq \int Q(z,a)dF(z) \leq \Alpha B  , :\:\ a \in \Lambda \end{equation}