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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Countably additive full conditional probabilities


Author: Thomas E. Armstrong
Journal: Proc. Amer. Math. Soc. 107 (1989), 977-987
MSC: Primary 60A10
MathSciNet review: 975631
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Abstract: Armstrong-Sudderth showed that a method of Carlson could be adapted to construct examples of countably additive full conditional probabilities. Here it is shown that all countably additive full conditional probabilities arise in this fashion. It is also shown that if the dimensionally ordered family of measures associated by Renyi to a full conditional probability contains an unbounded measure the full conditional probability fails to be countably additive. This leads to the notion of proper full conditional probabilities which if well founded in the sense of Krauss agree with the class of full conditional probabilities arising from Carlson's construction. Section 3 explores the connection between coherence of countable betting systems and countable additivity of full conditional probabilities.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0975631-6
PII: S 0002-9939(1989)0975631-6
Keywords: Full conditional probability, countable additivity, coherence
Article copyright: © Copyright 1989 American Mathematical Society