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<p>In this paper, we investigate the Weyl mean orbital pseudo-metric for Polish dynamical systems and its connections to the properties of the space of invariant measures. We establish equivalent conditions under which the set of invariant measures generated by periodic points is dense in the set of ergodic measures, thereby providing a deeper understanding of the relationship between periodic behavior and measure-theoretic properties in the field of Weyl mean orbital pseudo-metric.</p>

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A Remark on Empirical Measure within Weyl Mean Orbital Pseudo-metric

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Zhongxuan Yang,
  • Xiaojun Huang

摘要

In this paper, we investigate the Weyl mean orbital pseudo-metric for Polish dynamical systems and its connections to the properties of the space of invariant measures. We establish equivalent conditions under which the set of invariant measures generated by periodic points is dense in the set of ergodic measures, thereby providing a deeper understanding of the relationship between periodic behavior and measure-theoretic properties in the field of Weyl mean orbital pseudo-metric.