Local conditional entropy in measure for covers with respect to a fixed partition
Dynamical Systems
2018-05-09 v1
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}.
Keywords
Cite
@article{arxiv.1705.05292,
title = {Local conditional entropy in measure for covers with respect to a fixed partition},
author = {Pierre Paul Romagnoli},
journal= {arXiv preprint arXiv:1705.05292},
year = {2018}
}