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October, 1975 Weak Comparative Probability on Infinite Sets
Peter C. Fishburn
Ann. Probab. 3(5): 889-893 (October, 1975). DOI: 10.1214/aop/1176996277

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.

Citation

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Peter C. Fishburn. "Weak Comparative Probability on Infinite Sets." Ann. Probab. 3 (5) 889 - 893, October, 1975. https://doi.org/10.1214/aop/1176996277

Information

Published: October, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0314.60003
MathSciNet: MR400317
Digital Object Identifier: 10.1214/aop/1176996277

Subjects:
Primary: 60A05
Secondary: 06A10

Keywords: Comparative probability , finitely additive measures , partial order

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 5 • October, 1975
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