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 | References | Similar Articles | Additional Information
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
Keywords:
Translation invariant measure,
countably generated <IMG WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\sigma$">-algebra,
continuum hypothesis
Article copyright:
© Copyright 1983
American Mathematical Society