  We adapt arguments concerning information-theoretic convergence in the
Central Limit Theorem to the case of dependent random variables under
Rosenblatt mixing conditions. The key is to work with random variables
perturbed by the addition of a normal random variable, giving us good control
of the joint density and the mixing coefficient. We strengthen results of
Takano and of Carlen and Soffer to provide entropy-theoretic, not weak
convergence.
