Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
, Volume 66, Issue 2, pp 205226
First online:
The extent of nonconglomerability of finitely additive probabilities
 Mark J. SchervishAffiliated withStatistics Department, CarnegieMellon University
 , Teddy SeidenfeldAffiliated withStatistics Department, CarnegieMellon University
 , Joseph B. KadaneAffiliated withStatistics Department, CarnegieMellon University
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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.
 Title
 The extent of nonconglomerability of finitely additive probabilities
 Journal

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume 66, Issue 2 , pp 205226
 Cover Date
 198407
 DOI
 10.1007/BF00531529
 Print ISSN
 00443719
 Online ISSN
 14322064
 Publisher
 SpringerVerlag
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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