“…Probably the first papers dealing with quenched limit theorems for random dynamical systems are [36,37], and since then limit theorems for several classes of random dynamical systems were vastly studied. We refer to [3,5,15,16,17,21,22,20,18,28,30,31,51,52] for a partial list of relatively recent results of this kind. We note that in many of the examples these results are obtained for the unique measure µ such that µ ω is absolutely continuous with respect to m. However, some results hold true even for maps T ω : E ω → E σω ⊂ X which are defined on random subsets of X (see [38]), where in this case the most notable choice of µ ω is the, so called, random Gibbs measure (see [28,43]).…”