# Sh:732

• Bartoszyński, T., & Shelah, S. (2002). Perfectly meager sets and universally null sets. Proc. Amer. Math. Soc., 130(12), 3701–3711.
• 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)
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},
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}
}