Linear liftings for non - complete probability spaces

We show that it is consistent with ZFC that L(Y,B, ν) has no linear lifting for many non-complete probability spaces (Y,B, ν), in particular for Y = [0, 1], B = Borel subsets of Y , ν = usual Radon measure on B. AMS Subject Classification 1980 (1985 revision): Primary: 28A51 Secondary: 03E35 1) Research supported by UPEI Senate Grant no 602101, by the Research Institute for Mathematical Sciences at Bar-Ilan University, and by the Landau Center for Mathematical Research in Analysis (supported by the Minerva Foundation). The author would like to thank the organizers of the Winter Institute on the Set Theory of the Reals for their hospitality while part of this research was being carried out. 2) Partially supported by the Foundation for Basic Research of the Israel Academy of Science. Publication number 437.