Perfectly meager sets and universally null sets

by Bartoszynski and Shelah. [BrSh:732]
Proc American Math Soc, 2002
For a set of reals X : (a) X is perfectly meager (PM) if for every perfect set P subseteq R, P cap X is meager in P . (b) X is universal null (UN) if every Borel isomorphic image of X has Lebesgue measure zero. We show that it is consistent with ZFC that PM is a subset of UN.

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