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Lebesgue integral

In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the x-axis. The Lebesgue integral, named after French mathematician Henri Lebesgue, is one way to make this concept rigorous and to extend it to more general functions.

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Overview

Introduction

Definition

Example

Domain of integration

Limitations of the Riemann integral

Basic theorems of the Lebesgue integral

Alternative formulations

Limitations of Lebesgue integral

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Lebesgue integral

Nodes98
Edges97
Triples189
Avg. degree1.98
Density0.020408
Components1

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Lebesgue integral

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related to References · 150
Lebesgue integral → Addison-Wesley Publishing Company Inc, Advanced Mathematics, American Mathematical Society, An, Analysis, Applied Mathematics, Bartle, Bauer, Berberian, Berlin, Big Rudin, Bourbaki, Brooks/Cole Advanced Books, Brooks/Cole Mathematics Series, CA, Cambridge, Chapter, Chapters, Co, Daniell
related to Relation between the viewpoints · 10
Lebesgue integral → Conversely, Define, Intuitively, Lebesgue, One, Riemann, Suppose, The, The Lebesgue, Then
related to Limitations of Lebesgue integral · 8
Lebesgue integral → But, Dirichlet, Lebesgue, On, One, The, There, This
related to Via improper Riemann integral · 7
Lebesgue integral → As, Assuming, It, Lebesgue, Riemann, The Lebesgue, This
related to Intuitive interpretation · 5
Lebesgue integral → Folland, For, Lebesgue, Riemann, The
related to Via simple functions · 5
Lebesgue integral → In, Lebesgue, One, Simple, The
related to Definition · 2
Lebesgue integral → Lebesgue, The

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Important terminology

integral lebesgue functions function displaystyle measure riemann integration defined measurable theory mu int set real simple one non-negative mr integrable

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SubjectPredicateObjectConfidenceSrc
Fubini's theorem.Rudininstance ofbut does not treat material0.80text
Walterinstance ofbut does not treat material0.80text
Lebesgue integralrelated to DefinitionThe0.60section
Lebesgue integralrelated to DefinitionLebesgue0.60section
Lebesgue integralrelated to Intuitive interpretationFolland0.60section
Lebesgue integralrelated to Intuitive interpretationRiemann0.60section
Lebesgue integralrelated to Intuitive interpretationLebesgue0.60section
Lebesgue integralrelated to Intuitive interpretationFor0.60section
Lebesgue integralrelated to Intuitive interpretationThe0.60section
Lebesgue integralrelated to Limitations of Lebesgue integralThe0.60section
Lebesgue integralrelated to Limitations of Lebesgue integralLebesgue0.60section
Lebesgue integralrelated to Limitations of Lebesgue integralThere0.60section

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