The relationship between Popper spaces (conditional probability spaces thatsatisfy some regularity conditions), lexicographic probability systems (LPS's),and nonstandard probability spaces (NPS's) is considered. If countableadditivity is assumed, Popper spaces and a subclass of LPS's are equivalent;without the assumption of countable additivity, the equivalence no longerholds. If the state space is finite, LPS's are equivalent to NPS's. However, ifthe state space is infinite, NPS's are shown to be more general than LPS's.
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