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On a problem of Banach


Authors: Andrzej Pelc and Karel Prikry
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0718982-7
Keywords: Translation invariant measure, countably generated $ \sigma $-algebra, continuum hypothesis
Article copyright: © Copyright 1983 American Mathematical Society

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