# Preference orderings represented by coherent upper and lower conditional previsions

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## Abstract

Preference orderings assigned by coherent lower and upper conditional previsions are defined and they are considered to define maximal random variables and Bayes random variables. Sufficient conditions are given such that a random variable is maximal if and only if it is a Bayes random variable. In a metric space preference orderings represented by coherent lower and upper conditional previsions defined by Hausdorff inner and outer measures are given.

## Keywords

Preference ordering Coherent upper and lower conditional previsions Choquet integral Disintegration property Hausdorff outer measures## Notes

### Acknowledgements

The author is grateful to two anonymous referees for their comments.

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