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HANDMADE DENSITY SETS

Published online by Cambridge University Press:  21 March 2017

GEMMA CAROTENUTO
GEMMA CAROTENUTO*
Affiliation:
DIPARTIMENTO DI MATEMATICA UNIVERSITA’ DI SALERNO SALERNO, ITALY E-mail: gcarotenuto@unisa.it
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Abstract

Given a metric space (X , d), equipped with a locally finite Borel measure, a measurable set $A \subseteq X$ is a density set if the points where A has density 1 are exactly the points of A. We study the topological complexity of the density sets of the real line with Lebesgue measure, with the tools—and from the point of view—of descriptive set theory. In this context a density set is always in $\Pi _3^0$ . We single out a family of true $\Pi _3^0$ density sets, an example of true $\Sigma _2^0$ density set and finally one of true $\Pi _2^0$ density set.

Keywords

03E1528A05Lebesgue measuredensity

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 1 , March 2017 , pp. 208 - 223
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

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