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- W143814632 abstract "SUMMARY. We consider how an unconditional, finite-valued, finitely additive proba bility Pona countable set may localize its non-conglomerability (non-disintegrability). Non conglomerability, a characteristic of merely finitely additive probability, occurs when the uncon ditional probability of an event P.{E) lies outside the closed interval of conditional probability values, [infhen P(Eh), suphG7r P(Eh)], taken from a countable partition 7r = {hj : j = 1,...}. The problem we address is how to identify events and partitions where a finite-valued, finitely additive probability fails to satisfy conglomerability. We focus on the extreme case of 2-valued finitely additive prob abilities that are not countably additive. These are, equivalently, non-principal ultrafilters. Evidently, the challenge we face is that given a countable partition, at most one of its elements has positive probability under P. Thus, we must find ways of regulating the coherent condi tional probabilities, given null events, that cohere with the unconditional probability P. Our analysis of P proceeds by the use of combinatorial properties of the associated non-principal ultrafilter Up. We show that when ultrafilter Up is not minimal in the Rudin-Keisler partial order of ?(w)u>, we may locate a partition in which P fails to satisfy the conglomerability principle by examining (at most) countably many partitions. This result is then applied to finitely additive probabilities that assume only finitely many values. By contrast, if ultrafilter Up is Rudin-Keisler minimal, then P is simultaneously conglomerate in each finite collection of partitions, though not simultaneously conglomerate in all partitions." @default.
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- W143814632 date "1998-01-01" @default.
- W143814632 modified "2023-09-23" @default.
- W143814632 title "Non-Conglomerability for Finite-Valued, Finitely Additive Probability" @default.
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