An edition of The integral (2011)

The integral

a crux for analysis

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Last edited by ImportBot
February 26, 2022 | History
An edition of The integral (2011)

The integral

a crux for analysis

  • 0 Ratings
  • 0 Want to read
  • 0 Currently reading
  • 0 Have read

This book treats all of the most commonly used theories of the integral. After motivating the idea of integral, we devote a full chapter to the Riemann integral and the next to the Lebesgue integral. Another chapter compares and contrasts the two theories. The concluding chapter offers brief introductions to the Henstock integral, the Daniell integral, the Stieltjes integral, and other commonly used integrals. The purpose of this book is to provide a quick but accurate (and detailed) introduction to all aspects of modern integration theory. It should be accessible to any student who has had calculus and some exposure to upper division mathematics.

Publish Date
Publisher
Morgan & Claypool
Language
English
Pages
93

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Previews available in: English

Edition Availability
Cover of: The integral
The integral: a crux for analysis
2011, Morgan & Claypool
electronic resource : in English

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Book Details


Published in

San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA)

Table of Contents

1. Introduction
What is an integral
What is the Riemann integral
What is the Riemann integral good for
What is the Riemann integral not good for
What is the Lebesgue integral
What is the Lebesgue integral good for
What is the Lebesgue not good for
Exercises
2. The Riemann integral
The definition
Properties of the Riemann integral
Characterization of Riemann integrability
The fundamental theorem of calculus
Numerical techniques of integration
Introduction
The method of rectangles
The trapezoidal rule
Simpson's rule
Integration by parts
Exercises
3. The Lebesgue integral
Elementary measure theory
Measurable sets
The Lebesgue integral
Three big theorems about the Lebesgue integral
The Lebesgue spaces LP
The Riesz representation theorem
Product integration: Fubini's theorem
Three principles of Littlewood
Differentiation of integrals: covering lemmas and the Lebesgue theorem
Basic ideas
The maximal function
The concept of convergence in measure
Functions of bounded variation and absolute continuity
Exercises
4. Comparison of the Riemann and Lebesgue integrals
Any Riemann integrable function is Lebesgue integrable
Exercises
5. Other theories of the integral
The Daniell integral
The Riemann-Stieltjes integral
The Henstock-Kurzweil integral
Hausdorff measure
Haar measure
The fundamental theorem
Exercises
Bibliography
Author's biography
Index.

Edition Notes

Part of: Synthesis digital library of engineering and computer science.

Series from website.

Includes bibliographical references (p. 87) and index.

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

Also available in print.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Series
Synthesis lectures on mathematics and statistics -- # 9
Other Titles
Synthesis digital library of engineering and computer science.

Classifications

Dewey Decimal Class
515.42
Library of Congress
QA311 .K725 2011

The Physical Object

Format
[electronic resource] :
Number of pages
93

ID Numbers

Open Library
OL25547253M
Internet Archive
integralcruxfora00kran
ISBN 13
9781608456147, 9781608456130
OCLC/WorldCat
701813451

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February 26, 2022 Edited by ImportBot import existing book
July 1, 2019 Edited by MARC Bot import existing book
July 29, 2014 Created by ImportBot import new book