Descriptive set-theoretical properties of an abstract density operator

• Autorzy: Szymon Gła̧b
• Języki publikacji: EN

Abstrakty

EN

Let $$ \mathcal{K} $$(ℝ) stand for the hyperspace of all nonempty compact sets on the real line and let d ±(x;E) denote the (right- or left-hand) Lebesgue density of a measurable set E ⊂ ℝ at a point x∈ ℝ. In [3] it was proved that $$ \{ K \in \mathcal{K}(\mathbb{R}):\forall _x \in K(d^ + (x,K) = 1ord^ - (x,K) = 1)\} $$ is ⊓11-complete. In this paper we define an abstract density operator ⅅ± and we generalize the above result. Some applications are included.

Słowa kluczowe

EN

Density; Porosity; Coanalytic set; ⊓11-complete set

Kategorie tematyczne

• 03E15: Descriptive set theory
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 4
• Strony: 732-740

Daty

wydano

2009-12-01

online

2009-10-31

Twórcy

autor

Szymon Gła̧b

• Institute of Mathematics, Technical University of Łódź, Łódź, Poland

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0048-x