Mixingales on Riesz spaces

A mixingale is a stochastic process which combines properties of martingales and mixing sequences. McLeish introduced the term mixingale at the 4th Conference on Stochastic Processes and Application, at York University, Toronto, 1974, in the context of L 2 . In this paper we generalize the concept of a mixingale to the measure-free Riesz space setting (this generalizes all of the L p , 1 ≤ p ≤ ∞ variants) and prove that a weak law of large numbers holds for Riesz space mixingales. In the process we also generalize the concept of uniform integrability to the Riesz space setting.