Remarks on the theory of conditional probability: Some issues of finite versus countable additivity

In Vincent F. Hendricks, Stig Andur Pederson & Klaus Frovin Jørgensen (eds.), Probability Theory: Philosophy, Recent History and Relations to Science. Synthese Library, Kluwer (2001)
This paper discusses some differences between the received theory of regular conditional distributions, which is the countably additive theory of conditional probability, and a rival theory of conditional probability using the theory of finitely additive probability. The focus of the paper is maximally "improper" conditional probability distributions, where the received theory requires, in effect, that P{a: P = 0} = 1. This work builds upon the results of Blackwell and Dubins
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Rohit Parikh (2005). Conditional Probability and Defeasible Inference. Journal of Philosophical Logic 34 (1):97 - 119.

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