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Csörnyei, Marianna; Grahl, Jack and O'Neil, Toby C.
(2012).
DOI: https://doi.org/10.14321/realanalexch.37.2.0243
Abstract
A Lebesgue measurable set in the real line has Lebesgue density 0 or 1 at almost every point. Kolyada showed that there is a positive constant such that for non-trivial measurable sets there is at least one point with upper and lower densities lying in the interval
. Both Kolyada and later Szenes gave bounds for the largest possible value of this
. In this note we reduce the best known upper bound, disproving a conjecture of Szenes.
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About
- Item ORO ID
- 31519
- Item Type
- Journal Item
- ISSN
- 0147-1937
- Keywords
- Lebesgue upper density; Lebesgue lower density
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2012 Michigan State University Press
- Related URLs
- Depositing User
- Toby O'Neil