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.

**[1]**David Blackwell,*On a class of probability spaces*, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. II, University of California Press, Berkeley and Los Angeles, 1956, pp. 1–6. MR**0084882****[2]**David Blackwell and Lester E. Dubins,*On existence and non-existence of proper, regular, conditional distributions*, Ann. Probability**3**(1975), no. 5, 741–752. MR**0400320****[3]**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**, 10.1090/S0002-9939-1977-0425071-5**[4]**Lester E. Dubins,*Finitely additive conditional probabilities, conglomerability and disintegrations*, Ann. Probability**3**(1975), 89–99. MR**0358891****[5]**B. de Finetti,*Probability, induction, and statistics*, Wiley, New York, 1972.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1983-0699405-3

Keywords:
Conglomerability,
disintegrations,
finite additivity

Article copyright:
© Copyright 1983
American Mathematical Society