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Borel liftings of the measure algebra and the failure of the continuum hypothesis

1994
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Proceedings of the American Mathematical Society
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It is proved that the failure of the continuum hypothesis is consistent with the existence of a Borel lifting for the Lebesgue measure algebra and an embedding of the Lebesgue measure algebra into p(w) /finite. Let LM denote the field of Lebesgue measurable sets and let A be the ideal of measure zero sets. A (measurable) lifting of the measure algebra LM/A is any Boolean embedding /: LM/A -> LM such that /(a) e a for all a in LM/A. If, in addition, each /(a) is a Borel set, then / is called a

doi:10.1090/s0002-9939-1994-1176066-8
fatcat:mf3eh6wnznernbiiyq4m2shwqi