On a problem of Banach-Reference-Cited by-同舟云学术

On a problem of Banach

Published:1983 Issue:4 Volume:89 Page:608-610
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Pelc Andrzej,Prikry Karel

Abstract

Assuming the continuum hypothesis, we obtain a translation invariant version of the following result of E. Grzegorek: There are two countably generated σ \sigma -algebras on the interval [0, 1] such that both carry a nonatomic countably additive probability measure, but the σ \sigma -algebra generated by their union does not carry any such measure.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1983-089-04/S0002-9939-1983-0718982-7/S0002-9939-1983-0718982-7.pdf

Reference7 articles.

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2. Remarks on 𝜎-fields without continuous measures;Grzegorek, E.;Colloq. Math.,1978

3. Solution of a problem of Banach on 𝜎-fields without continuous measures;Grzegorek, Edward;Bull. Acad. Polon. Sci. S\'{e}r. Sci. Math.,1980

4. Construction of a non-separable invariant extension of the Lebesgue measure space;Kakutani, Shizuo;Ann. of Math. (2),1950

5. On discrete Borel spaces and projective sets;Rao, B. V.;Bull. Amer. Math. Soc.,1969

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