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Weak Comparative Probability on Infinite Sets

Peter C. Fishburn
The Annals of Probability
Vol. 3, No. 5 (Oct., 1975), pp. 889-893
Stable URL: http://www.jstor.org/stable/2959132
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Weak Comparative Probability on Infinite Sets
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Abstract

Let $\mathscr{J}$ be a Boolean algebra of subsets of a state space $S$ and let $\succ$ be a binary comparative probability relation on $\mathscr{J}$ with $A \succ B$ interpreted as "$A$ is more probable than $B$." Axioms are given for $\succ$ on $\mathscr{J}$ which are sufficient for the existence of a finitely additive probability measure $P$ on $\mathscr{J}$ which has $P(A) > P(B)$ whenever $A \succ B$. The axioms consist of a necessary cancellation or additivity condition, a simple monotonicity axiom, an axiom for the preservation of $\succ$ under common deletions, and an Archimedean condition.

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