English

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

R2 v1 2026-06-22T02:44:53.705Z