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arXiv · 1705.05292

Local conditional entropy in measure for covers with respect to a fixed partition

Pierre Paul Romagnoli
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Abstract

In this paper, we introduce two measure theoretical notions of conditional entropy for finite measurable covers conditioned to a finite measurable partition and prove that they are equal. Using this we state a local variational principle with respect to the notion of conditional entropy defined by Misiurewicz in \cite{M} for the case of open covers. This in particular extends the work done in \cite{R} and \cite{HYZ}.

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Pierre Paul Romagnoli. 2017-05-15. Local conditional entropy in measure for covers with respect to a fixed partition. https://doi.org/10.1088/1361-6544%2Faaaf49

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