With respect to tail sigma fields, standard measures possess measurable disintegrations
Authors:
Lester E. Dubins and David Heath
Journal:
Proc. Amer. Math. Soc. 88 (1983), 416-418
MSC:
Primary 28A50; Secondary 60A10
DOI:
https://doi.org/10.1090/S0002-9939-1983-0699405-3
MathSciNet review:
699405
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a countably additive probability on a standard space, and let
be a tail subfield. Though no disintegration of
with respect to
that is countably additive need exist, there always is one which is finitely additive.
- [1] David Blackwell, On a class of probability spaces, Proc. Third Berkeley Sympos. Math. Statist. and Prob. 1-6, University of California Press, Berkeley, Calif., 1955. MR 0084882 (18:940d)
- [2] David Blackwell and Lester E. Dubins, On existence and non-existence of proper, regular, conditional distributions, Ann. Probab. 3 (1975), 741-752. MR 0400320 (53:4155)
- [3] Lester E. Dubins, Measurable, tail disintegrations of the Haar integral are purely finitely additive, Proc. Amer. Math. Soc. 62 (1977), 34-36. MR 0425071 (54:13029)
- [4] -, Finitely additive conditional probabilities, conglomerability and disintegrations, Ann. Probab. 3 (1975), 89-99. MR 0358891 (50:11348)
- [5] B. de Finetti, Probability, induction, and statistics, Wiley, New York, 1972.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1983-0699405-3
Keywords:
Conglomerability,
disintegrations,
finite additivity
Article copyright:
© Copyright 1983
American Mathematical Society