TY - JOUR

T1 - On a problem of banach

AU - Pelc, Andrzej

AU - Prikry, Karel

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1983/12

Y1 - 1983/12

N2 - Assuming the continuum hypothesis, we obtain a translation invariant version of the following result of E. Grzegorek: There are two countably generated o-algebras on the interval [0, 1 ] such that both carry a nonatomic countably additive probability measure, but the a-algebra generated by their union does not carry any such measure.

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

KW - Continuum hypothesis

KW - Countably generated o-algebra

KW - Phrases. Translation invariant measure

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U2 - 10.1090/S0002-9939-1983-0718982-7

DO - 10.1090/S0002-9939-1983-0718982-7

M3 - Article

AN - SCOPUS:84966214695

VL - 89

SP - 608

EP - 610

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -