On Meager Additive and Null Additive Sets in the Cantor Space and in ℝ
Tomasz Weiss (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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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.