Given a sequence of random variables \(\xi_{1}, \xi_{2}, \ldots\), for which \(D \xi_{n} \leqslant C\) and \(R_{i j} \rightarrow 0\) as \(|i-j| \longrightarrow \infty\left(R_{i j}\right.\) is the correlation coefficient of \(\xi_{i}\) and \(\left.\xi_{j}\right)\), prove that the law of large numbers is applicable to this sequence (Bernstein's theorem).