Entropy of random dynamical systems (Q1084211)

Let (M,B,\(\mu)\) be a non-atomic Lebesgue space, (S,\({\mathcal S})\) be a standard measurable space and let \(f:S\times M\to M\) be measurable, such that for each \(s\in S\quad m\to f(s,m)\) is \(\mu\)-preserving. For a (strictly) stationary sequence \((\xi_ n)\) of S-valued random variables the random dynamical system is defined by \(X_ n=f(\xi_ n,X_{n- 1}),X_ 0=id_ M.\) The author then proves a.e. random versions of some classical theorems on entropy (e.g. Kolmogorov-Sinai, Shannon-McMillan, Katok, Kushnirenko).