Mixing inequalities in Riesz spaces

@article{Kuo2017MixingII,
  title={Mixing inequalities in Riesz spaces},
  author={Wen-Chi Kuo and Michael Rogans and Bruce A. Watson},
  journal={arXiv: Functional Analysis},
  year={2017}
}
Ergodicity in Riesz Spaces
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
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Strong convergence and convergence in probability were generalized to the setting of a Riesz space with conditional expectation operator, $T$, in [{{\sc Y. Azouzi, W.-C. Kuo, K. Ramdane, B. A.
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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
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We extend the Koopman-von Neumann convergence condition on the Ces\`{a}ro mean to the context of a Dedekind complete Riesz space with weak order unit. As a consequence, a characterisation of
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References

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Mixingales on Riesz spaces
Discrete stochastic integration in Riesz spaces
In this work we continue the developments of Kuo et al. (Indag Math 15:435–451, 2004; J Math Anal Appl 303:509–521, 2005) with the construction of the martingale transform or discrete stochastic
Convergence of Riesz space martingales
Discrete-time stochastic processes on Riesz spaces
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
Markov processes on Riesz spaces
Measure-free discrete time stochastic processes in Riesz spaces were formulated and studied by Kuo, Labuschagne and Watson. Aspects relating martingales, stopping times, convergence of these
Conditional expectations on Riesz spaces
Mixing: Properties and Examples
Mixing is concerned with the analysis of dependence between sigma-fields defined on the same underlying probability space. It provides an important tool of analysis for random fields, Markov
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