The Blackwell relation defines no lattice
Information Theory
2015-03-05 v1 math.IT
Statistics Theory
Statistics Theory
Abstract
Blackwell's theorem shows the equivalence of two preorders on the set of information channels. Here, we restate, and slightly generalize, his result in terms of random variables. Furthermore, we prove that the corresponding partial order is not a lattice; that is, least upper bounds and greatest lower bounds do not exist.
Cite
@article{arxiv.1401.3146,
title = {The Blackwell relation defines no lattice},
author = {Nils Bertschinger and Johannes Rauh},
journal= {arXiv preprint arXiv:1401.3146},
year = {2015}
}
Comments
5 pages, 1 figure