Skip to main content
×
Home
    • Aa
    • Aa

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.

Copyright
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
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

T. E Armstrong . & K Prikry . (1980). κ-finiteness and κ-additivity of measures on sets and left invariant measures on discrete groups. Proceedings of the American Mathematical Society, 80, 105112.

J. L Doob . (1994). Measure Theory. New York: Springer-Verlag.

L Dubins . (1975). Finitely additive conditional probabilities, conglomerability and disintegrations. Annals of Probability, 3, 8999.

P. R Halmos . (1950). Measure Theory. New York: Springer-Verlag.

J. B. Kadane , M. J. Schervish , & T Seidenfeld . (1996). Reasoning to a foregone conclusion. Journal of American Statistical Association, 91, 12281235.

A Kolmogorov . (1956). Foundations of the Theory of Probability. New York: Chelsea.

M. J. Schervish , T. Seidenfeld , & J. B Kadane . (1984). The extent of non-conglomerability of finitely additive probabilities. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 66(2), 205226.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 16 *
Loading metrics...

Abstract views

Total abstract views: 144 *
Loading metrics...

* Views captured on Cambridge Core between 27th December 2016 - 24th August 2017. This data will be updated every 24 hours.