## The Annals of Probability

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

Fred S. Roberts

#### 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

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