The Annals of Probability

Allocations of Probability

Glenn Shafer

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Abstract

This paper studies belief functions, set functions which are normalized and monotone of order $\infty$. The concepts of continuity and condensability are defined for belief functions, and it is shown how to extend continuous or condensable belief functions from an algebra of subsets to the corresponding power set. The main tool used in this extension is the theorem that every belief function can be represented by an allocation of probability--i.e., by a $\cap$ -homomorphism into a positive and completely additive probability algebra. This representation can be deduced either from an integral representation due to Choquet or from more elementary work by Revuz and Honeycutt.

Article information

Source
Ann. Probab., Volume 7, Number 5 (1979), 827-839.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994941

Digital Object Identifier
doi:10.1214/aop/1176994941

Mathematical Reviews number (MathSciNet)
MR542132

Zentralblatt MATH identifier
0414.60002

JSTOR
links.jstor.org

Subjects
Primary: 60A05: Axioms; other general questions
Secondary: 62A99: None of the above, but in this section

Keywords
Belief function allocation of probability capacity upper and lower probabilities condensability continuity

Citation

Shafer, Glenn. Allocations of Probability. Ann. Probab. 7 (1979), no. 5, 827--839. doi:10.1214/aop/1176994941. https://projecteuclid.org/euclid.aop/1176994941


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