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<p>We study the set of harmonic limits of empirical measures in topological dynamical systems. We obtain a characterization of unique ergodicity based on logarithmic (harmonic) mean convergence in place of Cesáro convergence. We introduce logarithmic mean equicontinuity and show that a topological dynamical system is logarithmically mean equicontinuous if and only if it is mean equicontinuous.</p>

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A Note on Logarithmic Mean Equicontinuity

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Dominik Kwietniak,
  • Jian Li,
  • Habibeh Pourmand

摘要

We study the set of harmonic limits of empirical measures in topological dynamical systems. We obtain a characterization of unique ergodicity based on logarithmic (harmonic) mean convergence in place of Cesáro convergence. We introduce logarithmic mean equicontinuity and show that a topological dynamical system is logarithmically mean equicontinuous if and only if it is mean equicontinuous.