Two Kinds of Invariance of Full Conditional Probabilities

• Autorzy: Pruss A. R.

Identyfikatory

DOI

10.4064/ba61-3-9

• 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.

Słowa kluczowe

EN

full conditional probability; G-invariance; left-orderable group; probability exchange rate

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: Vol. 61, no 3-4
• Strony: 277--283
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Pruss A. R.

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

Bibliografia

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