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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Measurable tail disintegrations of the Haar integral are purely finitely additive
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by Lester E. Dubins PDF
Proc. Amer. Math. Soc. 62 (1977), 34-36 Request permission

Abstract:

There are countably additive probability measures, P, and sub-sigma fields, relative to which P admits no proper, measurable, conditional distributions, except, possibly, those which are purely finitely additive. The usual fair, coin-tossing probability measure and the tail sigma field illustrate this phenomenon. More generally, every measurable, disintegration of the Haar integral of any compact metrizable group, G, relative to the partition, $\Pi$, of G which consists of the left cosets of any dense denumerable subgroup S of G, or what comes to the same thing, relative to the sigma field of Haar-measurable subsets of G which are invariant under right translation by S, is purely finitely additive.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 62 (1977), 34-36
  • MSC: Primary 28A50; Secondary 60A10, 22C05
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0425071-5
  • MathSciNet review: 0425071