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

T. Carlson, R. Frankiewicz, P. Zbierski
1994 Proceedings of the American Mathematical Society  
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
more » ... hen / is called a Borel lifting. It is known (see [M]) that each measure algebra of a rj-finite measure has a measurable lifting. In [N-S] it is proved that CH (the continuum hypothesis)
doi:10.1090/s0002-9939-1994-1176066-8 fatcat:mf3eh6wnznernbiiyq4m2shwqi