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Addendum to "On Meager Additive and Null Additive Sets in the Cantor space $2^{ω}$ and in ℝ" (Bull. Polish Acad. Sci. Math. 57 (2009), 91-99)

100%

Weiss T.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

tom 62

nr 1

1-9

We prove in ZFC that there is a set $A ⊆ 2^{ω}$ and a surjective function H: A → ⟨0,1⟩ such that for every null additive set X ⊆ ⟨0,1), $H^{-1}(X)$ is null additive in $2^ω$. This settles in the affirmative a question of T. Bartoszyński.

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

100%

Weiss T.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

tom 57

nr 2

91-99

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 $2^{ω}$ if{f} 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.

Ograniczanie wyników

2 Bulletin of the Polish Academy of Sciences. Mathematics

2 Weiss T.

1 2014

1 2009

Wyniki wyszukiwania

Addendum to "On Meager Additive and Null Additive Sets in the Cantor space $2^{ω}$ and in ℝ" (Bull. Polish Acad. Sci. Math. 57 (2009), 91-99)

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