The Lebesgue Differentiation Theorem via nonoverlapping interval covers

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A short proof is given for the Lebesgue Differentiation Theorem using a variation of the Heine-Borel covering property, without reliance on sophisticated approaches such as Vitali covers and the rising sun lemma.

Original languageEnglish (US)
Pages (from-to)953-956
Number of pages4
JournalReal Analysis Exchange
Volume29
Issue number2
StatePublished - 2004

Fingerprint

Covering Properties
Henri Léon Lebésgue
Sun
Lemma
Cover
Interval
Theorem

Keywords

  • Interval cover
  • Lebesgue differentiation theorem
  • Monotone function

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

Cite this

The Lebesgue Differentiation Theorem via nonoverlapping interval covers. / Hagood, John W.

In: Real Analysis Exchange, Vol. 29, No. 2, 2004, p. 953-956.

Research output: Contribution to journalArticle

@article{82c30aef641b412a8a412c58d1f7806e,
title = "The Lebesgue Differentiation Theorem via nonoverlapping interval covers",
abstract = "A short proof is given for the Lebesgue Differentiation Theorem using a variation of the Heine-Borel covering property, without reliance on sophisticated approaches such as Vitali covers and the rising sun lemma.",
keywords = "Interval cover, Lebesgue differentiation theorem, Monotone function",
author = "Hagood, {John W}",
year = "2004",
language = "English (US)",
volume = "29",
pages = "953--956",
journal = "Real Analysis Exchange",
issn = "0147-1937",
publisher = "Michigan State University Press",
number = "2",

}

TY - JOUR

T1 - The Lebesgue Differentiation Theorem via nonoverlapping interval covers

AU - Hagood, John W

PY - 2004

Y1 - 2004

N2 - A short proof is given for the Lebesgue Differentiation Theorem using a variation of the Heine-Borel covering property, without reliance on sophisticated approaches such as Vitali covers and the rising sun lemma.

AB - A short proof is given for the Lebesgue Differentiation Theorem using a variation of the Heine-Borel covering property, without reliance on sophisticated approaches such as Vitali covers and the rising sun lemma.

KW - Interval cover

KW - Lebesgue differentiation theorem

KW - Monotone function

UR - http://www.scopus.com/inward/record.url?scp=32844474303&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=32844474303&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:32844474303

VL - 29

SP - 953

EP - 956

JO - Real Analysis Exchange

JF - Real Analysis Exchange

SN - 0147-1937

IS - 2

ER -