Weak ergodicity of stationary pairwise independent processes

It is proven that a stationary process of pairwise independent random varia bles with values in a separable metric space is weakly ergodic, i.e. each r andom variable is independent of the system of invariant sets of the proces s. An example shows that a process of identically distributed pairwise inde pendent random variables is in general, however, not weakly ergodic.