Title :
The Blackwell relation defines no lattice
Author :
Bertschinger, Nils ; Rauh, Johannes
Author_Institution :
Max Planck Inst. for Math. in the Sci., Leipzig, Germany
fDate :
June 29 2014-July 4 2014
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.
Keywords :
information theory; statistics; Blackwell relation; Blackwell theorem; information channel; preorder equivalence; Generators; Information theory; Lattices; Markov processes; Random variables; Upper bound; Vectors;
Conference_Titel :
Information Theory (ISIT), 2014 IEEE International Symposium on
Conference_Location :
Honolulu, HI
DOI :
10.1109/ISIT.2014.6875280
