Ergodic theory and the Strong Law of Large Numbers on Riesz spaces

In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435–451], we introduced the concepts of conditional expectations, martingales and stopping times on Riesz spaces. Here we formulate and prove order theoretic analogues of the Birkhoff, Hopf andWiener ergodic theorems and the Strong Law of Large Numbers on Riesz spaces (vector lattices). © 2006 Elsevier Inc. All rights reserved.