Home > Iowa Academy of Science > Journals & Newsletters > Proceedings of the Iowa Academy of Science > Volume 65 (1958) > Annual Issue
Document Type
Research
Abstract
Lebesgue's density theorem states that at almost every point of a measurable set S in En, the metric density of S exists and is 1 and at almost every point of the complement of S, the density of S exists and is 0. This theorem was first proven for E1 by Lebesgue using his theory of integration. It was later proven by Denjoy [1], Lusin [2], and Sierpinski [3] for E1 without the use of integration. The theorem was first proven for En by de la Vallee Poussin.
Publication Date
1958
Journal Title
Proceedings of the Iowa Academy of Science
Volume
65
Issue
1
First Page
335
Last Page
339
Copyright
©1958 Iowa Academy of Science, Inc.
Language
en
File Format
application/pdf
Recommended Citation
Martin, N. F. G.
(1958)
"Exceptional Values of Metric Density,"
Proceedings of the Iowa Academy of Science, 65(1), 335-339.
Available at:
https://scholarworks.uni.edu/pias/vol65/iss1/49