  A notion of dynamical entropy for discrete-time stochastic processes with
values in arbitrary measurable spaces is introduced. It turns out that the
entropy of the stochastic process defined by iterations of a measure-preserving
transformation coincides with (ordinary) entropy of the transformation. More
generally, it is shown that the entropy of any stationary process coincides
with (ordinary) entropy of shift transformation on the path-space associated to
the process. Various basic properties of this notion are considered. A
variational inequality for topological entropy of arbitrary subsets of infinite
product spaces is given.
