Allocations of Probability
| Autor: | Glenn Shafer |
|---|---|
| Rok vydání: | 1979 |
| Předmět: |
condensability
Discrete mathematics Statistics and Probability 62A99 capacity upper and lower probabilities Law of total probability Function (mathematics) Extension (predicate logic) continuity Power set Belief function allocation of probability Combinatorics Monotone polygon Set function Upper and lower probabilities Statistics Probability and Uncertainty Representation (mathematics) 60A05 Mathematics |
| Zdroj: | Classic Works of the Dempster-Shafer Theory of Belief Functions ISBN: 9783540253815 Ann. Probab. 7, no. 5 (1979), 827-839 |
| ISSN: | 0091-1798 |
| DOI: | 10.1214/aop/1176994941 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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