Abstract. In a largely overlooked paper of Murray Rosenblatt from more than thirty years ago, it was shown that if a strictly stationary Markov chain satisfies ``uniform ergodicity" as well as mixing (in the ergodic-theoretic sense), then it satisfies the (Rosenblatt) strong mixing condition. In this note, a strengthened version of that theorem will be presented. As a by-product, a couple of other, somewhat hidden, insights in that paper of Rosenblatt will be brought into sharper focus.

AMS Subject Classification (1991): 60G10, 60J05

Keyword(s): strong mixing, uniform ergodicity, Markov chain

Received July 30, 2008. (Registered under 6078/2009.)