An empirical central limit theorem for dependent sequences

We prove a central limit theorem for the dd-dimensional distribution function of a class of stationary sequences. The conditions are expressed in terms of some coefficients which measure the dependence between a given σσ-algebra and indicators of quadrants. These coefficients are weaker than the corresponding mixing coefficients, and can be computed in many situations. In particular, we show that they are well adapted to functions of mixing sequences, iterated random functions, and a class of dynamical systems.