Ergodicity in Riesz Spaces

  title={Ergodicity in Riesz Spaces},
  author={Jonathan Homann and Wen-Chi Kuo and Bruce Alastair Watson},
  journal={arXiv: Dynamical Systems},
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… 
1 Citations

Characterisation of conditional weak mixing via ergodicity of the tensor product in Riesz Spaces

We link conditional weak mixing and ergodicity of the tensor product in Riesz spaces. In particular, we characterise conditional weak mixing of a conditional expectation preserving system by the



A Koopman-von Neumann type theorem on the convergence of Cesàro means in Riesz spaces

We extend the Koopman-von Neumann convergence condition on the Cesàro mean to the context of a Dedekind complete Riesz space with weak order unit. As a consequence, a characterisation of conditional

Limit laws for martingales in vector lattices

  • G. Stoica
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2019

An Andô-Douglas type theorem in Riesz spaces with a conditional expectation

In this paper we formulate and prove analogues of the Hahn-Jordan decomposition and an Andô-Douglas-Radon-Nikodým theorem in Dedekind complete Riesz spaces with a weak order unit, in the presence of

Infinite Dimensional Analysis: A Hitchhiker’s Guide

This text was born out of an advanced mathematical economics seminar at Caltech in 1989-90. We realized that the typical graduate student in mathematical economics has to be familiar with a vast