Two Kinds of Invariance of Full Conditional Probabilities

• Autorzy: Alexander R. Pruss
• Języki publikacji: EN

Abstrakty

EN

Let G be a group acting on Ω and ℱ a G-invariant algebra of subsets of Ω. A full conditional probability on ℱ is a function P: ℱ × (ℱ∖{∅}) → [0,1] satisfying the obvious axioms (with only finite additivity). It is weakly G-invariant provided that P(gA|gB) = P(A|B) for all g ∈ G and A,B ∈ ℱ, and strongly G-invariant provided that P(gA|B) = P(A|B) whenever g ∈ G and A ∪ gA ⊆ B. Armstrong (1989) claimed that weak and strong invariance are equivalent, but we shall show that this is false and that weak G-invariance implies strong G-invariance for every Ω, ℱ and P as above if and only if G has no non-trivial left-orderable quotient. In particular, G = ℤ provides a counterexample to Armstrong's claim.

Kategorie tematyczne

• 60B99: None of the above, but in this section
• 06F15: Ordered groups
• 60A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: 61
• Numer: 3
• Strony: 277-283

Daty

wydano

2013

Twórcy

autor

Alexander R. Pruss

• Department of Philosophy, Baylor University, One Bear Place #97273, Waco, TX 76798-7273, U.S.A.

Identyfikatory

DOI

10.4064/ba61-3-9