Lebesgue Integration and Measure

By: No Information Available

Write A Review

Paperback | 9 July 1973

At a Glance

Paperback
296 Pages

Dimensions(cm)
15.3 x 22.9 x 2.4

Paperback

RRP $119.95

$114.99

or 4 interest-free payments of $28.75 with

or

Ships in 15 to 25 business days

Lebesgue integration is a technique of great power and elegance which can be applied in situations where other methods of integration fail. It is now one of the standard tools of modern mathematics, and forms part of many undergraduate courses in pure mathematics.

Dr Weir's book is aimed at the student who is meeting the Lebesgue integral for the first time. Defining the integral in terms of step functions provides an immediate link to elementary integration theory as taught in calculus courses. The more abstract concept of Lebesgue measure, which generalises the primitive notions of length, area and volume, is deduced later.

The explanations are simple and detailed with particular stress on motivation. Over 250 exercises accompany the text and are grouped at the ends of the sections to which they relate: notes on the solutions are given.

Industry Reviews

'The book is easy to read, partly because of the treatment adopted, and partly because of the quality of the exposition. Dr Weir's style is clear, friendly and informal; he shows how the results fit in with the reader's intuition; he highlights the important things and warns of the difficult things (these warnings when a hard bit is coming up are most confidence-preserving). He does not aim at maximum generality at the cost of understanding. The examples are chosen with care, many of them being, in effect, lemmas that will be needed later in the proofs of theorems.' Mathematical Gazette

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Calculus & Mathematical Analysis

A Visual Approach to Introductory Functional Analysis

Hardcover

RRP $200.00

$176.75

12%
OFF

The Maths Book

Big Ideas Simply Explained

Hardcover

RRP $45.00

$35.75

21%
OFF

Artificial Intelligence in Modeling and Simulation : Simulation Foundations, Methods and Applications - Philippe Giabbanelli

$145.75

19%
OFF

Calculus Essentials For Dummies

For Dummies

Paperback

RRP $21.95

$19.75

10%
OFF

Calculus For Dummies

For Dummies

Paperback

RRP $37.95

$30.75

19%
OFF

Calculus All-in-One For Dummies (+ Chapter Quizzes Online)

For Dummies

Paperback

RRP $65.95

$49.75

25%
OFF

Calculus, Metric Edition

9th edition

Paperback

RRP $184.95

$148.75

20%
OFF

Essential Calculus

2nd Edition

Hardcover

RRP $219.95

$173.75

21%
OFF

Introduction to Finite Element Analysis Using MATLAB® and Abaqus

Hardcover

RRP $395.00

$190.99

52%
OFF

Intermediate Financial Theory

3rd Edition

Hardcover

RRP $195.75

$190.99

Learning Data Science

Data Wrangling, Exploration, Visualization, and Modeling with Python

Paperback

RRP $171.00

$82.99

51%
OFF

Bird's Engineering Mathematics

9th Edition

Paperback

RRP $110.00

$83.99

24%
OFF

Ordinary Differential Equations : Basic Methods, Qualitative Theory, And Fun Models - Michail Zhitomirskii

$73.75

51%
OFF

Mastering Shiny

Build Interactive Apps, Reports, and Dashboards Powered by R

Paperback

RRP $152.00

$73.75

51%
OFF

An Introduction To Derivative Securities, Financial Markets, And Risk Management

2nd edition

Paperback

RRP $158.99

$68.75

57%
OFF

Cartoon Guide to Calculus

Cartoon Guide Series

Paperback

RRP $31.89

$29.75

Data Science on AWS

Implementing End-To-End, Continuous AI and Machine Learning Pipelines

Paperback

RRP $152.00

$73.75

51%
OFF

Preface	p. ix
The Completeness of the Reals	p. 1
The Axiom of Completeness	p. 2
Infima and suprema	p. 8
Postscript on the axioms for R	p. 11
Null Sets	p. 15
Countable sets	p. 15
Null sets	p. 18
Cantor's ternary set	p. 20
The Lebesgue Integral on R	p. 22
Step functions	p. 23
Construction of the Lebesgue integral	p. 30
Relation to the 'definite integral'	p. 44
Relation to the 'indefinite integral'	p. 54
Some further results	p. 63
The Lebesgue Integral on R	p. 70
Step functions on R	p. 70
The Lebesgue integral on R	p. 77
Fubini's Theorem	p. 83
The Convergence Theorems	p. 93
The Monotone Convergence Theorem	p. 94
The Dominated Convergence Theorem	p. 106
Measurable Functions and Lebesgue Measure	p. 119
Measurable functions	p. 119
Lebesgue measure on R	p. 124
The geometry of Lebesgue measure	p. 134
Transformation of integrals	p. 146
The Spaces L[superscript p]	p. 162
The completeness of R as a metric space	p. 162
The spaces L[superscript p]	p. 164
The geometry of L[superscript 2]	p. 172
Bounded linear functionals on L[suprescript 2]	p. 181
Orthonormal sets in L[superscript 2]	p. 188
Classical Fourier series	p. 202
Reflections on Hilbert space	p. 219
The elements of topology	p. 223
Solutions	p. 241
References	p. 277
Index	p. 279
Table of Contents provided by Syndetics. All Rights Reserved.

Lebesgue Integration and Measure

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Calculus & Mathematical Analysis

A Visual Approach to Introductory Functional Analysis

The Maths Book

Big Ideas Simply Explained

Artificial Intelligence in Modeling and Simulation

Simulation Foundations, Methods and Applications

Differential Equations

An Elementary Approach

Advances in Numerical Methods and Analysis

Introductory Numerical Analysis

Calculus

9th edition - Early Transcendentals, Metric

Calculus Essentials For Dummies

For Dummies

Calculus For Dummies

For Dummies

Calculus All-in-One For Dummies (+ Chapter Quizzes Online)

For Dummies

Calculus, Metric Edition

9th edition

Essential Calculus

2nd Edition

Introduction to Finite Element Analysis Using MATLAB® and Abaqus

Intermediate Financial Theory

3rd Edition

Learning Data Science

Data Wrangling, Exploration, Visualization, and Modeling with Python

Bird's Engineering Mathematics

9th Edition

Ordinary Differential Equations

Basic Methods, Qualitative Theory, And Fun Models

Learning Algorithms

A Programmer's Guide to Writing Better Code

Mastering Shiny

Build Interactive Apps, Reports, and Dashboards Powered by R

An Introduction To Derivative Securities, Financial Markets, And Risk Management

2nd edition

Cartoon Guide to Calculus

Cartoon Guide Series

Data Science on AWS

Implementing End-To-End, Continuous AI and Machine Learning Pipelines

Infinite Powers

How Calculus Reveals the Secrets of the Universe

Vectors and Spaces

A Complete Guide to Linear Algebra

This product is categorised by