Descriptive set-theoretical properties of an abstract density operator
Szymon Gła̧b
Open Mathematics, Tome 7 (2009), p. 732-740 / Harvested from The Polish Digital Mathematics Library
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Let 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∈𝒦(ℝ):∀x∈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.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:269147 
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     title = {Descriptive set-theoretical properties of an abstract density operator},
     journal = {Open Mathematics},
     volume = {7},
     year = {2009},
     pages = {732-740},
     zbl = {1185.28001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0048-x}
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Szymon Gła̧b. Descriptive set-theoretical properties of an abstract density operator. Open Mathematics, Tome 7 (2009) pp. 732-740. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0048-x/

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