The extent of nonconglomerability of finitely additive probabilities
 Mark J. Schervish,
 Teddy Seidenfeld,
 Joseph B. Kadane
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An arbitrary finitely additive probability can be decomposed uniquely into a convex combination of a countably additive probability and a purely finitely additive (PFA) one. The coefficient of the PFA probability is an upper bound on the extent to which conglomerability may fail in a finitely additive probability with that decomposition. If the probability is defined on a σfield, the bound is sharp. Hence, nonconglomerability (or equivalently nondisintegrability) characterizes finitely as opposed to countably additive probability. Nonetheless, there exists a PFA probability which is simultaneously conglomerable over an arbitrary finite set of partitions.
Neither conglomerability nor nonconglomerability in a given partition is closed under convex combinations. But the convex combination of PFA ultrafilter probabilities, each of which cannot be made conglomerable in a common margin, is singular with respect to any finitely additive probability that is conglomerable in that margin.
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 Title
 The extent of nonconglomerability of finitely additive probabilities
 Journal

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume 66, Issue 2 , pp 205226
 Cover Date
 19840701
 DOI
 10.1007/BF00531529
 Print ISSN
 00443719
 Online ISSN
 14322064
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 Mark J. Schervish ^{(1)}
 Teddy Seidenfeld ^{(1)}
 Joseph B. Kadane ^{(1)}
 Author Affiliations

 1. Statistics Department, CarnegieMellon University, 15213, Pittsburgh, PA, USA