Preorderings compatible with probability measures
Rolando Chuaqui, Jerome I. Malitz · Transactions of the American Mathematical Society · 1983
The main theorem proved in this paper is: Let B B be a σ \sigma -complete Boolean algebra and ≽ a \succcurlyeq a binary relation with field B B such that: (i) Every finite subalgebra B ′ B’ admits a probability measure μ ′ \mu ’ such that for p , q ∈ B ′ , p ≽ q i f f μ ′ p ⩾ μ ′ q p,q \in B’,p \succcurlyeq q\;iff\mu ’p \geqslant \mu ’q . (ii) If for every i , p i , q ∈ B i,{p_i},q \in B and p i ⊆ p i + 1 ≼ q {p_i} \subseteq {p_{i + 1}} \preccurlyeq q , then ∪ i > ∞