## The Annals of Probability

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

### Allocations of Probability

#### 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