On Meager Additive and Null Additive Sets in the Cantor Space $2^{\omega }$ and in ℝ

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 57.2 (2009): 91-99. <http://eudml.org/doc/286629>.

@article{TomaszWeiss2009,
abstract = {Let T be the standard Cantor-Lebesgue function that maps the Cantor space $2^\{ω\}$ onto the unit interval ⟨0,1⟩. We prove within ZFC that for every $X ⊆ 2^\{ω\}$, X is meager additive in $2^\{ω\}$ 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 $2^\{ω\}$ and ℝ.},
author = {Tomasz Weiss},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {meager additive set; null additive set; Cantor space; real line},
language = {eng},
number = {2},
pages = {91-99},
title = {On Meager Additive and Null Additive Sets in the Cantor Space $2^\{ω\}$ and in ℝ},
url = {http://eudml.org/doc/286629},
volume = {57},
year = {2009},
}

TY - JOUR
AU - Tomasz Weiss
TI - On Meager Additive and Null Additive Sets in the Cantor Space $2^{ω}$ and in ℝ
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2009
VL - 57
IS - 2
SP - 91
EP - 99
AB - Let T be the standard Cantor-Lebesgue function that maps the Cantor space $2^{ω}$ onto the unit interval ⟨0,1⟩. We prove within ZFC that for every $X ⊆ 2^{ω}$, X is meager additive in $2^{ω}$ 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 $2^{ω}$ and ℝ.
LA - eng
KW - meager additive set; null additive set; Cantor space; real line
UR - http://eudml.org/doc/286629
ER -