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T-topologies on a lattice ordered group.

Montserrat Pons (1982)

Stochastica

In this paper a characterization of the topologies on a l-group arising from a CTRO (T-topologies) is given. We use it to find conditions under which the Redfield topology comes from a CTRO.

Two Kinds of Invariance of Full Conditional Probabilities

Alexander R. Pruss (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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...

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