Sufficient Conditions for the Existence of Disintegrations

Patrizia Berti () and Pietro Rigo ()
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Patrizia Berti: Università di Firenze
Pietro Rigo: Università di Firenze

Journal of Theoretical Probability, 1999, vol. 12, issue 1, 75-86

Abstract: 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.

Keywords: Analytic set; cardinality; disintegration; finite additivity; proper regular conditional distribution; sufficient statistic (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1021792409934

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