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June, 1973 A Note on Fine's Axioms for Qualitative Probability
Fred S. Roberts
Ann. Probab. 1(3): 484-487 (June, 1973). DOI: 10.1214/aop/1176996942


Fine gives axioms on a binary relation $\precsim$ on a field of events, with $A \precsim B$ interpreted as "$A$ is (subjectively) no more probable than $B$," sufficient to guarantee the existence of an order-preserving probability measure and an additive order-preserving probability measure. It is noted that one of Fine's axioms, that the order topology have a countable base, can be replaced by the more appealing axiom that there is a countable order-dense subset.


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Fred S. Roberts. "A Note on Fine's Axioms for Qualitative Probability." Ann. Probab. 1 (3) 484 - 487, June, 1973.


Published: June, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0289.60003
MathSciNet: MR358890
Digital Object Identifier: 10.1214/aop/1176996942

Primary: 60A05
Secondary: 06A45

Keywords: order topology , qualitative probability , subjective probability

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 3 • June, 1973
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