# 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.

- published version (11p)

Bib entry

@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}, doi = {10.1090/S0002-9939-02-06465-1}, mrclass = {03E15 (03E35)}, mrnumber = {1920051}, mrreviewer = {Jakub Jasi\'nski}, 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} }