ISSN:
1572-9230
Keywords:
Analytic set
;
cardinality
;
disintegration
;
finite additivity
;
proper regular conditional distribution
;
sufficient statistic
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let $${\text{(}}\Omega {\text{,}}A,,P)$$ be a probability space and Π a partition of Ω. A necessary and sufficient condition is given for the existence of a σ-additive and measurable disintegration of P on Π. It is also shown that P admits a σ-additive (but not measurable) disintegration on Π whenever $${\text{(}}\Omega {\text{,}}A,,)$$ is a standard space and the set (ω1, ω2):ω1 and ω2 are in the same element of Π} is coanalytic in Ω×Ω. Finally, sufficient statistics (in the classical Fisherian sense) are investigated by using σ-additive disintegrations as conditional probabilities.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1021792409934
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