Abstract. In this paper, we continue development of the theory of contractive Markov systems initiated in Werner (J. Lond. Math. Soc. at press). We prove an ergodic theorem for Markov chains associated with such systems using the coding map constructed in Werner (2003 Preprint). This is a generalization of the ergodic theorem of Elton (1987 Ergod. Theory Dyn. Syst. 7 481–8).

Mathematics Subject Classification: 28D05, 28A80, 37H99, 60J05, 60G10

Print publication: Issue 6 (November 2004)
Received 14 May 2004, in final form 19 August 2004
Published 9 September 2004