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On a Problem of Banach
Andrzej Pelc and Karel Prikry
Proceedings of the American Mathematical Society
Vol. 89, No. 4 (Dec., 1983), pp. 608-610
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2044591
Page Count: 3
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Assuming the continuum hypothesis, we obtain a translation invariant version of the following result of E. Grzegorek: There are two countably generated σ-algebras on the interval [ 0, 1 ] such that both carry a nonatomic countably additive probability measure, but the σ-algebra generated by their union does not carry any such measure.
Proceedings of the American Mathematical Society © 1983 American Mathematical Society