The Lebesgue differentiation theorem via the rising sun lemma
type: Item
instance of: scholarly article
title: The Lebesgue differentiation theorem via the rising sun lemma
zbMATH Open document ID: 1076.26004
author: C. Faure
published in: Real Analysis Exchange
publication date: 2005-04-04T00:00:00Z
review text: An elegant proof of Lebesgue's differentiation theorem is obtained using a version of the rising sun lemma for continuous functions and a reduction of the main statement to the continuous case, based on the fact that a strictly increasing function on an interval has a continuous inverse. Only basic properties of Lebesgue outer measure are needed, making this a suitable approach for an elementary course.
Mathematics Subject Classification ID: 26A24
Mathematics Subject Classification ID: 26A48
Mathematics Subject Classification ID: 28A12
zbMATH DE Number: 2151959
zbMATH Keywords: Lebesgue differentiation theorem
zbMATH Keywords: monotone function
reviewed by: J. W. Hagood
MaRDI profile type: Publication
full work available at URL: realanalexch.29.2.0947
OpenAlex ID: W1550125810
DOI: 10.14321/REALANALEXCH.29.2.0947
description: scientific article; zbMATH DE number 2151959