Optimal quality of exceptional points for the Lebesgue density theorem
- 78 Downloads
In spite of the Lebesgue density theorem, there is a positive δ such that, for every non-trivial measurable set S⊂ℝ, there is a point at which both the lower densities of S and of ℝ∖S are at least δ. The problem of determining the supremum of possible values of this δ was studied in a paper of V. I. Kolyada, as well as in some recent papers. We solve this problem in the present work.
Key words and phrasesLebesgue density theorem exceptional point interval configuration
2010 Mathematics Subject Classification28A99
Unable to display preview. Download preview PDF.
- M. Csörnyei, J. Grahl and T. C. O’Neil, Points of middle density in the real line, preprint, available e.g. at http://www.homepages.ucl.ac.uk/~ucahmcs/publ/index.html.