Let S be a set and B be a $sigma$-field on S. We consider $(Omega = S^Z, T = B^z, P)$ as the basic probability space. We denote by T the left shift on $Omega$. We assume that P is invariant under T, i.e., $PT^{-1} = P$, and that T is ergodic. We denote by $X = cdots, X_-1, X_0, X_1, cdots$ the coordinate maps on $Omega$. From our assumptions it follows that ${X_i}_{i in Z}$ is a stationary and ergodic process.