# Ergodicity in Riesz Spaces

@article{Homann2020ErgodicityIR, title={Ergodicity in Riesz Spaces}, author={Jonathan Homann and Wen-Chi Kuo and Bruce Alastair Watson}, journal={arXiv: Dynamical Systems}, year={2020} }

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…

## One Citation

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

- Mathematics
- 2021

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…

## References

SHOWING 1-10 OF 17 REFERENCES

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

- MathematicsProceedings of the American Mathematical Society, Series B
- 2021

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…

### The Hájek-Rényi-Chow maximal inequality and a strong law of large numbers in Riesz spaces

- MathematicsJournal of Mathematical Analysis and Applications
- 2020

### Limit laws for martingales in vector lattices

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

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

- Mathematics
- 2009

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

- Economics
- 1994

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…