Csörnyei, Marianna; Grahl, Jack and O'Neil, Toby C.
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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.
|Item Type:||Journal Article|
|Copyright Holders:||2012 Michigan State University Press|
|Keywords:||Lebesgue upper density; Lebesgue lower density|
|Academic Unit/Department:||Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
|Depositing User:||Toby O'Neil|
|Date Deposited:||29 Nov 2012 10:13|
|Last Modified:||06 Oct 2016 00:19|
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