English

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}
}