2022 The Density of Borel Sets
T.H. Steele
Author Affiliations +
Real Anal. Exchange 47(2): 371-376 (2022). DOI: 10.14321/realanalexch.47.2.1633455391

Abstract

Using a novel approach, we develop a result analogous to the Lebesgue density theorem for Borel sets using the notion of category: If $B\subset \lbrack 0,1]$ is a Borel set, then there exists a first category set $S\subset B$ with the property that for every $x\in B-S$ there exists $\varepsilon >0$ such that $B\cap (x-\varepsilon ,x+\varepsilon )$ is a residual subset of $(x-\varepsilon ,x+\varepsilon )$.

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T.H. Steele. "The Density of Borel Sets." Real Anal. Exchange 47 (2) 371 - 376, 2022. https://doi.org/10.14321/realanalexch.47.2.1633455391

Information

Published: 2022
First available in Project Euclid: 10 February 2023

Digital Object Identifier: 10.14321/realanalexch.47.2.1633455391

Subjects:
Primary: 28A05
Secondary: 54B30 , 54H05

Keywords: Borel set , density point , measurable set , Residual set

Rights: Copyright © 2022 Michigan State University Press

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Vol.47 • No. 2 • 2022
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