Abstract
AbstractThe ergodic theorems of Hopf, Wiener and Birkhoff were extended to the context of Riesz spaces with a weak order unit and conditional expectation operator by Kuo, Labuschagne and Watson in [Ergodic Theory and the Strong Law of Large Numbers on Riesz Spaces. J Math Anal Appl 325 (2007), 422–437]. However, the precise concept of what constitutes ergodicity in Riesz spaces was not considered. In this short paper we fill in this omission and give some explanations of the choices made. In addition, we consider the interplay between mixing and ergodicity in the Riesz space setting.KeywordsErgodicityRiesz spacesWeak mixingConditional expectation operators Mathematics Subject Classification (2010) Primary 46A40; 47A35; Secondary 37A25; 60F05
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