Lexicographic Probability, Conditional Probability, and Nonstandard Probability
CORNELL UNIV ITHACA NY DEPT OF COMPUTER SCIENCE
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The relationship between Popper spaces conditional probability spaces that satisfy some regularity conditions, lexicographic probability systems LPSs Blume, Brandenburger, and Dekel 1991a Blume, Brandenburger, and Dekel 1991b, and nonstandard probability spaces NPSs is considered. If countable additivity is assumed, Popper spaces and a subclass of LPSs are equivalent without the assumption of countable additivity, the equivalence no longer holds. If the state space is finite, LPSs are equivalent to NPSs. However, if the state space is infinite, NPSs are shown to be more general than LPSs.
- Statistics and Probability