Lexicographic probability, conditional probability, and nonstandard probability

The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS's), and nonstandard probability spaces (NPS's) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS'...

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Bibliographic Details
Published in:Games and economic behavior 2010, Vol.68 (1), p.155-179
Main Author: Halpern, Joseph Y.
Format: Article
Language:English
Subjects:
Correlation analysis
Game theory
Measurement
Probability
Probability distribution
Studies
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Summary:The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS's), and nonstandard probability spaces (NPS's) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS's are equivalent; without the assumption of countable additivity, the equivalence no longer holds. If the state space is finite, LPS's are equivalent to NPS's. However, if the state space is infinite, NPS's are shown to be more general than LPS's.
ISSN:0899-8256
1090-2473
DOI:10.1016/j.geb.2009.03.013