About the Berry-Esseen theorem for weakly dependent sequences

We extend the method of Bergstrom for the rates of convergence in the central limit theorem to weakly dependent sequences. In particular, we prove that, for stationary and uniformly mixing sequences of real-valued and bounded random variables, the rate of convergence in the central limit theorem is of the order of n(-1/2) as soon as the sequence (theta(p))(p>0) of uniform mixing coefficients satisfies Sigma(p>0)p theta(p) < infinity.