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Proceedings of the American Mathematical Society

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On universal null sets

Authors: E. Grzegorek and C. Ryll-Nardzewski
Journal: Proc. Amer. Math. Soc. 81 (1981), 613-617
MSC: Primary 04A15; Secondary 28A05
MathSciNet review: 601741
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Abstract: If all subsets of cardinality less than $ {2^{{\aleph _0}}}$ of the real line $ R$ are Lebesgue measurable then there exists a permutation $ p$ of $ R$ with $ p = {p^{ - 1}}$ such that on the $ \sigma $-field generated by $ \mathcal{B} \cup p(\mathcal{B})$ there is no continuous probability measure.

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Keywords: $ \sigma $-field of sets, continuous measure, Lebesgue measure, universal null set, universally measurable set, Borel set, universally measurable function, bimeasurable function, continuum hypothesis, Martin's Axiom
Article copyright: © Copyright 1981 American Mathematical Society

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