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
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by Lester E. Dubins and David Heath PDF

Proc. Amer. Math. Soc. 88 (1983), 416-418 Request permission

Abstract:

Let $P$ be a countably additive probability on a standard space, and let $\mathcal {A}$ be a tail subfield. Though no disintegration of $P$ with respect to $\mathcal {A}$ that is countably additive need exist, there always is one which is finitely additive.

References

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Probability, induction, and statistics