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NONCONGLOMERABILITY FOR COUNTABLY ADDITIVE MEASURES THAT ARE NOT κ-ADDITIVE

  • MARK J. SCHERVISH (a1), TEDDY SEIDENFELD (a2) and JOSEPH B. KADANE (a1)
Abstract
Abstract

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes a result of Schervish, Seidenfeld, & Kadane (1984), which established that each finite but not countably additive probability has conditional probabilities that fail to be conglomerable in some countable partition.

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Corresponding author
*STATISTICS DEPARTMENT CARNEGIE MELLON UNIVERSITY PITTSBURGH, PA 15213, USA E-mail: mark@stat.cmu.edu
PHILOSOPHY & STATISTICS DEPARTMENTS CARNEGIE MELLON UNIVERSITY PITTSBURGH, PA 15213, USA E-mail: teddy@stat.cmu.edu
STATISTICS DEPARTMENT CARNEGIE MELLON UNIVERSITY PITTSBURGH, PA 15213, USA E-mail: kadane@stat.cmu.edu
References
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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