Ergodicity in Riesz spaces

2020/10/13 by Jonathan Homann, Homann, Jonathan, Wen-Chi Kuo +3
Mathematics · #37A25 #46A40 #47A35 #60F05 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.DS #math.FA #math.PR #msc:37A25 #msc:46A40 #msc:47A35 #msc:60F05

paper · pdf · doi:10.48550/arxiv.2010.07206

arxiv created 2020/10/20 · arxiv updated 2020/10/21

Abstract

The 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. Journal of Mathematical Analysis and Applications, 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.

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