Mixing properties of a class of Bernoulli-processes

We prove that stationary very weak Bernoulli processes with rate O(1/n) (VWB O(1/n)) are strictly very weak Bernoulli with rate O(1/n). Furthermore we discuss the relation between VWB O(1/n) and the classical mixing properties for countable state processes. In particular, we show that VWB O(1/n) implies φ-mixing