The Annals of Probability

A Note on Fine's Axioms for Qualitative Probability

Fred S. Roberts

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Abstract

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.

Article information

Source
Ann. Probab., Volume 1, Number 3 (1973), 484-487.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996942

Digital Object Identifier
doi:10.1214/aop/1176996942

Mathematical Reviews number (MathSciNet)
MR358890

Zentralblatt MATH identifier
0289.60003

JSTOR
links.jstor.org

Subjects
Primary: 60A05: Axioms; other general questions
Secondary: 06A45

Keywords
Subjective probability qualitative probability order topology

Citation

Roberts, Fred S. A Note on Fine's Axioms for Qualitative Probability. Ann. Probab. 1 (1973), no. 3, 484--487. doi:10.1214/aop/1176996942. https://projecteuclid.org/euclid.aop/1176996942


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Corrections

  • Correction: Fred S. Roberts. Correction Note: Correction to "A Note on Fine's Axioms for Qualitative Probability". Ann. Probab., Vol. 2, Iss. 1 (1974), 182.