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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

© Copyright 1958 by the Iowa Academy of Science, Inc.

Language

EN

File Format

application/pdf

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