UNIGE document Scientific Article
previous document  unige:16440  next document
add to browser collection
Title

Exceptional points for Lebesgue's density theorem on the real line

Author
Published in Advances in Mathematics. 2011, vol. 226, no. 1, p. 764-778
Abstract For a nontrivial measurable set on the real line, there are always exceptional points, where the lower and upper densities of the set are neither 0 nor 1. We quantify this statement, following work by V. Kolyada, and obtain the unexpected result that there is always a point where the upper and the lower densities are closer to 1/2 than to zero or one. The method of proof uses a discretized restatement of the problem, and a self-similar construction.
Keywords Lebesgue density theoremMeasurable setsFractalsInterval configurations
Stable URL http://archive-ouverte.unige.ch/unige:16440
Full text
Identifiers
Structures

216 hits

2 downloads

Update

Deposited on : 2011-06-27

Export document
Format :
Citation style :