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<p>The conditional supremum, a parallel notion to the conditional expectation, was introduced by Barron, Cardaliaguet, and Jensen and has since been used in various results in measure theory. Recently this concept was extended to the framework of Riesz spaces and was used to characterize specific financial conditions. As promised in an earlier work, we leverage this operator to characterize ergodicity, a fundamental notion in dynamical systems. Our results generalize and improve previous findings established within the probabilistic framework. Additionally, we introduce the notion of irreducibility in Riesz spaces and connect it to ergodicity.</p>

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Ergodicity via conditional supremum and irreducibility in Riesz spaces

  • 期刊论文

  • 发表日期：

    2025年11月7日

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  • Youssef Azouzi,
  • Marwa Masmoudi

摘要

The conditional supremum, a parallel notion to the conditional expectation, was introduced by Barron, Cardaliaguet, and Jensen and has since been used in various results in measure theory. Recently this concept was extended to the framework of Riesz spaces and was used to characterize specific financial conditions. As promised in an earlier work, we leverage this operator to characterize ergodicity, a fundamental notion in dynamical systems. Our results generalize and improve previous findings established within the probabilistic framework. Additionally, we introduce the notion of irreducibility in Riesz spaces and connect it to ergodicity.