The Annals of Statistics
- Ann. Statist.
- Volume 9, Number 3 (1981), 658-662.
Agreeing Probability Measures for Comparative Probability Structures
It is proved that fine and tight comparative probability structures (where the set of events is assumed to be an algebra, not necessarily a $\sigma$-algebra) have agreeing probability measures. Although this was often claimed in the literature, all proofs the author encountered are not valid for the general case, but only for $\sigma$-algebras. Here the proof of Niiniluoto (1972) is supplemented. Furthermore an example is presented that reveals many misunderstandings in the literature. At the end a necessary and sufficient condition is given for comparative probability structures to have an almost agreeing probability measure.
Ann. Statist., Volume 9, Number 3 (1981), 658-662.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Wakker, Peter. Agreeing Probability Measures for Comparative Probability Structures. Ann. Statist. 9 (1981), no. 3, 658--662. doi:10.1214/aos/1176345469. https://projecteuclid.org/euclid.aos/1176345469