  A mixingale is a stochastic process which combines properties of martingales
and mixing sequences. McLeish introduced the term mixingale at the $4^{th}$
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 $L^p, 1\le p\le \infty$ 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.
