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October, 1979 Allocations of Probability
Glenn Shafer
Ann. Probab. 7(5): 827-839 (October, 1979). DOI: 10.1214/aop/1176994941


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.


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Glenn Shafer. "Allocations of Probability." Ann. Probab. 7 (5) 827 - 839, October, 1979.


Published: October, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0414.60002
MathSciNet: MR542132
Digital Object Identifier: 10.1214/aop/1176994941

Primary: 60A05
Secondary: 62A99

Keywords: allocation of probability , belief function , capacity , condensability , continuity , upper and lower probabilities

Rights: Copyright © 1979 Institute of Mathematical Statistics


Vol.7 • No. 5 • October, 1979
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