Abstract: | Let (Ω, µ) be a shift of finite type with a Markov probability, and (Y, ν) a non-atomic standard measure space. For each symbol i of the symbolic space, let Φi be a non-singular automorphism of (Y, ν). We study skew products of the form (ω, y) ? (σω, Φω0 (y)), where σ is the shift map on (Ω, µ). We prove that, when the skew product is recurrent, it is ergodic if and only if the Φi’s have no common non-trivial invariant set. |