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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
MathSciNet review:
699405
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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.
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David
Blackwell, On a class of probability spaces, Proceedings of
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(18,940d)
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David
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E. Dubins, On existence and non-existence of proper, regular,
conditional distributions, Ann. Probability 3 (1975),
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Lester
E. Dubins, Measurable tail disintegrations of the
Haar integral are purely finitely additive, Proc. Amer. Math. Soc. 62 (1976), no. 1, 34–36 (1977). MR 0425071
(54 #13029), http://dx.doi.org/10.1090/S0002-9939-1977-0425071-5
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Lester
E. Dubins, Finitely additive conditional probabilities,
conglomerability and disintegrations, Ann. Probability
3 (1975), 89–99. MR 0358891
(50 #11348)
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B. de Finetti, Probability, induction, and statistics, Wiley, New York, 1972.
- [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:
http://dx.doi.org/10.1090/S0002-9939-1983-0699405-3
PII:
S 0002-9939(1983)0699405-3
Keywords:
Conglomerability,
disintegrations,
finite additivity
Article copyright:
© Copyright 1983 American Mathematical Society
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