With respect to tail sigma fields, standard measures possess measurable disintegrations

Dubins, Lester E.; Heath, David

doi:10.1090/S0002-9939-1983-0699405-3

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a countably additive probability on a standard space, and let $\mathcal{A}$ be a tail subfield. Though no disintegration of with respect to $\mathcal{A}$ 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, https://doi.org/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.