TY - JOUR
T1 - On a problem of banach
AU - Pelc, Andrzej
AU - Prikry, Karel
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
SN - 0002-9939
VL - 89
SP - 608
EP - 610
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 4
ER -