A Note on Exchangeable Sequences.
STANFORD UNIV CALIF DEPT OF STATISTICS
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If X sub 1,X sub 2,... is an exchangeable sequence taking values in a complete, separable metric space, then there is a random variable M such that i given M, X sub 1,X sub 2,... are conditionally independent and identically distributed ii if X sub 1,X sub 2,... are conditionally independent and identically distributed given the random object Y, then a version of M is measurable with respect to the sigma-field spanned by Y iii the sigma-field spanned by M coincides as a measure algebra with the invariant, tail, and exchangeable sigma-fields of the process X sub 1,X sub 2,... , even though none of the latter three is countably generated. Author
- Statistics and Probability