The extent of non-conglomerability of finitely additive probabilities
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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 σ-field, the bound is sharp. Hence, non-conglomerability (or equivalently non-disintegrability) 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 non-conglomerability 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.
- The extent of non-conglomerability of finitely additive probabilities
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume 66, Issue 2 , pp 205-226
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Industry Sectors