The Blackwell relation defines no lattice

Published 14 Jan 2014 in cs.IT, math.IT, math.ST, and stat.TH | (1401.3146v1)

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.

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