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

Tomasz Weiss — 2009

Bulletin of the Polish Academy of Sciences. Mathematics

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 $X \subseteq 2^{ω}$ , 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.

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)

Tomasz Weiss — 2014

Bulletin of the Polish Academy of Sciences. Mathematics

We prove in ZFC that there is a set $A \subseteq 2^{ω}$ 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.

A note on the intersection ideal $ℳ \cap 𝒩$

Tomasz Weiss — 2013

Commentationes Mathematicae Universitatis Carolinae

We prove among other theorems that it is consistent with $Z F C$ that there exists a set $X \subseteq 2^{ω}$ which is not meager additive, yet it satisfies the following property: for each $F_{σ}$ measure zero set $F$ , $X + F$ belongs to the intersection ideal $ℳ \cap 𝒩$ .

More remarks on the intersection ideal $ℳ \cap 𝒩$

Tomasz Weiss — 2018

Commentationes Mathematicae Universitatis Carolinae

We prove in ZFC that every $ℳ \cap 𝒩$ additive set is $𝒩$ additive, thus we solve Problem 20 from paper [Weiss T., A note on the intersection ideal $ℳ \cap 𝒩$ , Comment. Math. Univ. Carolin. 54 (2013), no. 3, 437-445] in the negative.

On the sharpness of the Stolz approach.

Di Biase, Fausto; Stokolos, Alexander; Svensson, Olof; Weiss, Tomasz — 2006

Annales Academiae Scientiarum Fennicae. Mathematica

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

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)

A note on the intersection ideal $ℳ \cap 𝒩$

More remarks on the intersection ideal $ℳ \cap 𝒩$

On the sharpness of the Stolz approach.

Advanced Search

Formula preview

Currently displaying 1 – 5 of 5

On Meager Additive and Null Additive Sets in the Cantor Space 2 ω and in ℝ

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)

A note on the intersection ideal ℳ ∩ 𝒩

More remarks on the intersection ideal ℳ ∩ 𝒩

On the sharpness of the Stolz approach.

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

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)

A note on the intersection ideal $ℳ \cap 𝒩$

More remarks on the intersection ideal $ℳ \cap 𝒩$