Liftings for Haar measure on (0,1)K

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Title Liftings for Haar measure on (0,1)K
Author(s) Maxim R. Burke, W. Just
Journal Israel Journal of Mathematics
Date 1991
Volume 73
Issue 1
Start page 33
End page 44
Abstract We call E subset-of-or-is-equal-to {0,1}kappa projective if for some countable A subset-of-or-is-equal-to kappa there is an E(A) subset-of-or-is-equal-to {0,1}A such that E = E(A) x {0,1}kappa/A and E(A) is a projective subset of the Cantor set {0,1}A. We construct a model where Haar measure on {0,1}kappa has no projective lifting (and in particular no Baire lifting) for any kappa greater-than-or-equal-to omega.

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