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

• Autorzy: Tomasz Weiss
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E05: Other combinatorial set theory
• 03E15: Descriptive set theory
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: 57
• Numer: 2
• Strony: 91-99

Daty

wydano

2009

Twórcy

autor

Tomasz Weiss

• Instytut Matematyki, Akademia Podlaska, 08-110 Siedlce, Poland

Identyfikatory

DOI

10.4064/ba57-2-1