  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.
