Measure theoretical entropy of covers
Dynamical Systems
2008-10-24 v1
Abstract
In this paper we introduce three notions of measure theoretical entropy of a measurable cover U in a measure theoretical dynamical system. Two of them were already introduced in [R] and the new one is defined only in the ergodic case. We then prove that these three notions coincide, thus answering a question posed in [R] and recover a variational inequality (proved in [GW]) and a proof of the classical variational principle based on a comparison between the entropies of covers and partitions.
Cite
@article{arxiv.0810.4300,
title = {Measure theoretical entropy of covers},
author = {Uri Shapira},
journal= {arXiv preprint arXiv:0810.4300},
year = {2008}
}
Comments
19 pages