Open Access
February, 1985 The Existence of Regular Conditional Probabilities: Necessary and Sufficient Conditions
Arnold M. Faden
Ann. Probab. 13(1): 288-298 (February, 1985). DOI: 10.1214/aop/1176993081


Different necessary and sufficient conditions for the existence of regular conditional probabilities are found for the cases of countably generated, countably separated, and complete probability spaces. Perfection is $n.$ and $s.$ for countably generated spaces, "almost pre-standardness" for the countably generated and countably separated cases, and discreteness for complete spaces. Several different forms of the regular conditional probability property must be distinguished.


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Arnold M. Faden. "The Existence of Regular Conditional Probabilities: Necessary and Sufficient Conditions." Ann. Probab. 13 (1) 288 - 298, February, 1985.


Published: February, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0593.60002
MathSciNet: MR770643
Digital Object Identifier: 10.1214/aop/1176993081

Primary: 60A10
Secondary: 60A28

Keywords: conditional probability , discrete measures , disintegrations , perfect measures , regular conditional probability , standard measures

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 1 • February, 1985
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