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<p>We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences. We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence. We also establish the Katok’s entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.</p>

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A formula of conditional entropy for metrics induced by probability bi-sequences

  • 期刊论文

  • 发表日期：

    2025年4月8日

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  • M. Rahimi,
  • N. Bidabadi

摘要

We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences. We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence. We also establish the Katok’s entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.