Let T be the standard Cantor-Lebesgue function that maps the Cantor space onto the unit interval ⟨0,1⟩. We prove within ZFC that for every , X is meager additive in iff T(X) is meager additive in ⟨0,1⟩. As a consequence, we deduce that the cartesian product of meager additive sets in ℝ remains meager additive in ℝ × ℝ. In this note, we also study the relationship between null additive sets in and ℝ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-2-1,
author = {Tomasz Weiss},
title = {On Meager Additive and Null Additive Sets in the Cantor Space $2^{$\omega$}$ and in $\mathbb{R}$},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {57},
year = {2009},
pages = {91-99},
zbl = {1188.03030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-2-1}
}
Tomasz Weiss. On Meager Additive and Null Additive Sets in the Cantor Space $2^{ω}$ and in ℝ. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 91-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-2-1/