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Title: On the topological complexity of the density sets of the real line
Authors: Carotenuto, Gemma
Longobardi, Patrizia
Gerla, Giangiacomo
Andretta, Alessandro
Keywords: Descriptive set theory
Topological complexity
Issue Date: 13-May-2015
Publisher: Universita degli studi di Salerno
Abstract: Given a metric space (X, d), equipped with a Borel measure, a measurable set A ⊆ X is a density set if the points where A has density 1 are exactly the points of A. The main theme of this work is the study of the topological complexity of the density sets of the real line with the Lebesgue measure, and it is carried out with the tools - and from the point of view - of descriptive set theory. In this context a density set is always in Π03, i.e. it is a countable intersection of sets in Fσ. We construct examples of true Π03 density sets and an example of true Σ02 density sets. Moreover, we find density sets in each class of the form (n-Π01)￿, that is the dual class of the differences of n-many closed sets. These results are obtained through two different strategies: one which is completely combinatorial in nature, and another one based on results which are analogous to the ones on the Cantor space in [1]. [edited by Author]
Description: 2012 - 2013
Appears in Collections:Matematica

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tesi_G.Carotenuto.pdftesi di dottorato1,52 MBAdobe PDFView/Open
abstract_in_inglese_e_in_italiano_G.Carotenuto.pdfabstract a cura dell'autore105,58 kBAdobe PDFView/Open

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