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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a problem of Banach
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by Andrzej Pelc and Karel Prikry
Proc. Amer. Math. Soc. 89 (1983), 608-610
DOI: https://doi.org/10.1090/S0002-9939-1983-0718982-7

Abstract:

Assuming the continuum hypothesis, we obtain a translation invariant version of the following result of E. Grzegorek: There are two countably generated $\sigma$-algebras on the interval [0, 1] such that both carry a nonatomic countably additive probability measure, but the $\sigma$-algebra generated by their union does not carry any such measure.
References
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Bibliographic Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 608-610
  • MSC: Primary 28C10; Secondary 04A20, 04A30
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0718982-7
  • MathSciNet review: 718982