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Descriptive set-theoretical properties of an abstract density operator

  • Research Article
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Central European Journal of Mathematics

Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics, Technical University of Łódź, Łódź, Poland

    Szymon Gła̧b

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  1. Szymon Gła̧b
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Correspondence to Szymon Gła̧b.

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Gła̧b, S. Descriptive set-theoretical properties of an abstract density operator. centr.eur.j.math. 7, 732–740 (2009). https://doi.org/10.2478/s11533-009-0048-x

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