## The Annals of Probability

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

### A Note on Fine's Axioms for Qualitative Probability

#### 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

#### 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.Project Euclid: euclid.aop/1176996768