Abstract
For a homeomorphism T on a compact metric space X, a T-invariant Borel probability measure \(\mu \) on X and a measure-theoretic quasifactor \({\widetilde{\mu }}\) of \(\mu \), we study the relationship between the local entropy of the system \((X,\mu ,T)\) and of its induced system \(({\mathcal {M}}(X),{\widetilde{\mu }},{\widetilde{T}})\), where \({\widetilde{T}}\) is the homeomorphism induced by T on the space \({\mathcal {M}}(X)\) of all Borel probability measures defined on X.
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The author would like to thank Nilson Bernardes Jr. and the anonymous referees for valuable comments that improved the text.
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Vermersch, R.M. Measure-Theoretic Uniformly Positive Entropy on the Space of Probability Measures. Qual. Theory Dyn. Syst. 23, 29 (2024). https://doi.org/10.1007/s12346-023-00892-y
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DOI: https://doi.org/10.1007/s12346-023-00892-y