Descriptive set-theoretical properties of an abstract density operator

Let (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 is ⊓ 1 1 -complete. In this paper we define an abstract density operator ⅅ ± and...

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Veröffentlicht in:	Central European journal of mathematics 2009-12, Vol.7 (4), p.732-740
1. Verfasser:	Gła̧b, Szymon
Format:	Artikel
Sprache:	eng
Schlagworte:	03E15 11-complete set 28A05 Algebra Coanalytic set Density Geometry Hyperspaces Lie Groups Mathematics Mathematics and Statistics Number Theory Porosity Probability Theory and Stochastic Processes Research Article Topological Groups
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Beschreibung
Zusammenfassung:	Let (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 is ⊓ 1 1 -complete. In this paper we define an abstract density operator ⅅ ± and we generalize the above result. Some applications are included.
ISSN:	1895-1074 2391-5455 1644-3616 2391-5455
DOI:	10.2478/s11533-009-0048-x