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Conditioning (updating) non-additive measures. (English) Zbl 0812.90001

Several update rules for non-additive probabilities, among them the Dempster-Shafer rule for belief functions and certain update rules in the spirit of Bayesian statistics with multiple prior probabilities, are reviewed, investigated and compared with each other. This is done within the unifying framework of general, nonadditive measure and integration theory. The methods exposed here are capable of generalizing conditional expectation of random variables to the submodular or supermodular case at least if the given algebra is finite.
Reviewer: D.Denneberg

MSC:

91B06 Decision theory
28A12 Contents, measures, outer measures, capacities
62C10 Bayesian problems; characterization of Bayes procedures
28A25 Integration with respect to measures and other set functions
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