Countably additive full conditional probabilities

Author:
Thomas E. Armstrong

Journal:
Proc. Amer. Math. Soc. **107** (1989), 977-987

MSC:
Primary 60A10

DOI:
https://doi.org/10.1090/S0002-9939-1989-0975631-6

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:
https://doi.org/10.1090/S0002-9939-1989-0975631-6

Keywords:
Full conditional probability,
countable additivity,
coherence

Article copyright:
© Copyright 1989
American Mathematical Society