A FORMULA OF CONDITIONAL ENTROPY FOR METRICS INDUCED BY PROBABILITY BI-SEQUENCES

doi:10.1007/s10473-025-0420-3

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (4): 1619-1639.doi: 10.1007/s10473-025-0420-3

A FORMULA OF CONDITIONAL ENTROPY FOR METRICS INDUCED BY PROBABILITY BI-SEQUENCES

M. RAHIMI^*, N. BIDABADI

Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran

收稿日期:2023-03-07 出版日期:2025-10-10 发布日期:2025-10-10

A FORMULA OF CONDITIONAL ENTROPY FOR METRICS INDUCED BY PROBABILITY BI-SEQUENCES

M. RAHIMI^*, N. BIDABADI

Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran

Received:2023-03-07 Online:2025-10-10 Published:2025-10-10
Contact: ^*M. RAHIMI, E-mail: m10.rahimi@gmail.com
About author:N. BIDABADI, E-mail: n_bidabadi90@yahoo.com

摘要/Abstract

摘要： Westudytheconditional 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 Katoks entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.

关键词: entropy, conditional entropy, probability bi-sequence

Abstract: Westudytheconditional 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 Katoks entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.

Key words: entropy, conditional entropy, probability bi-sequence

M. RAHIMI, N. BIDABADI. A FORMULA OF CONDITIONAL ENTROPY FOR METRICS INDUCED BY PROBABILITY BI-SEQUENCES[J]. 数学物理学报(英文版), 2025, 45(4): 1619-1639.

M. RAHIMI, N. BIDABADI. A FORMULA OF CONDITIONAL ENTROPY FOR METRICS INDUCED BY PROBABILITY BI-SEQUENCES[J]. Acta mathematica scientia,Series B, 2025, 45(4): 1619-1639.

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A FORMULA OF CONDITIONAL ENTROPY FOR METRICS INDUCED BY PROBABILITY BI-SEQUENCES

A FORMULA OF CONDITIONAL ENTROPY FOR METRICS INDUCED BY PROBABILITY BI-SEQUENCES

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