Sh:732

• Bartoszyński, T., & Shelah, S. (2002). Perfectly meager sets and universally null sets. Proc. Amer. Math. Soc., 130(12), 3701–3711. arXiv: math/0102011 DOI: 10.1090/S0002-9939-02-06465-1 MR: 1920051
• Abstract:
  For a set of reals X: (a) X is perfectly meager (PM) if for every perfect set P\subseteq{\mathbb 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.

• Version 2001-07-14_11 (10p) published version (11p)

@article{Sh:732,
 author = {Bartoszy{\'n}ski, Tomek and Shelah, Saharon},
 title = {{Perfectly meager sets and universally null sets}},
 journal = {Proc. Amer. Math. Soc.},
 fjournal = {Proceedings of the American Mathematical Society},
 volume = {130},
 number = {12},
 year = {2002},
 pages = {3701--3711},
 issn = {0002-9939},
 mrnumber = {1920051},
 mrclass = {03E15 (03E35)},
 doi = {10.1090/S0002-9939-02-06465-1},
 note = {\href{https://arxiv.org/abs/math/0102011}{arXiv: math/0102011}},
 arxiv_number = {math/0102011},
 keyword = {perfectly meager, universally null,  consistency}
}