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A User-Friendly Introduction to Lebesgue Measure and Integration

Gail S. Nelson Carleton College, Northfield, MN
Available Formats:
Softcover ISBN: 978-1-4704-2199-1
Product Code: STML/78
List Price: $52.00 Individual Price:$41.60
Electronic ISBN: 978-1-4704-2737-5
Product Code: STML/78.E
List Price: $49.00 Individual Price:$39.20
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List Price: $78.00 Click above image for expanded view A User-Friendly Introduction to Lebesgue Measure and Integration Gail S. Nelson Carleton College, Northfield, MN Available Formats:  Softcover ISBN: 978-1-4704-2199-1 Product Code: STML/78  List Price:$52.00 Individual Price: $41.60  Electronic ISBN: 978-1-4704-2737-5 Product Code: STML/78.E  List Price:$49.00 Individual Price: $39.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$78.00
• Book Details

Student Mathematical Library
Volume: 782015; 221 pp
MSC: Primary 26; 28;

A User-Friendly Introduction to Lebesgue Measure and Integration provides a bridge between an undergraduate course in Real Analysis and a first graduate-level course in Measure Theory and Integration. The main goal of this book is to prepare students for what they may encounter in graduate school, but will be useful for many beginning graduate students as well. The book starts with the fundamentals of measure theory that are gently approached through the very concrete example of Lebesgue measure. With this approach, Lebesgue integration becomes a natural extension of Riemann integration.

Next, $L^p$-spaces are defined. Then the book turns to a discussion of limits, the basic idea covered in a first analysis course. The book also discusses in detail such questions as: When does a sequence of Lebesgue integrable functions converge to a Lebesgue integrable function? What does that say about the sequence of integrals? Another core idea from a first analysis course is completeness. Are these $L^p$-spaces complete? What exactly does that mean in this setting?

This book concludes with a brief overview of General Measures. An appendix contains suggested projects suitable for end-of-course papers or presentations.

The book is written in a very reader-friendly manner, which makes it appropriate for students of varying degrees of preparation, and the only prerequisite is an undergraduate course in Real Analysis.

Undergraduate and graduate students and researchers interested in learning and teaching real analysis.

• Chapters
• Chapter 0. Review of Riemann integration
• Chapter 1. Lebesgue measure
• Chapter 2. Lebesgue integration
• Chapter 3. $L^p$ spaces
• Chapter 4. General measure theory
• Ideas for projects

• Request Review Copy
• Get Permissions
Volume: 782015; 221 pp
MSC: Primary 26; 28;

A User-Friendly Introduction to Lebesgue Measure and Integration provides a bridge between an undergraduate course in Real Analysis and a first graduate-level course in Measure Theory and Integration. The main goal of this book is to prepare students for what they may encounter in graduate school, but will be useful for many beginning graduate students as well. The book starts with the fundamentals of measure theory that are gently approached through the very concrete example of Lebesgue measure. With this approach, Lebesgue integration becomes a natural extension of Riemann integration.

Next, $L^p$-spaces are defined. Then the book turns to a discussion of limits, the basic idea covered in a first analysis course. The book also discusses in detail such questions as: When does a sequence of Lebesgue integrable functions converge to a Lebesgue integrable function? What does that say about the sequence of integrals? Another core idea from a first analysis course is completeness. Are these $L^p$-spaces complete? What exactly does that mean in this setting?

This book concludes with a brief overview of General Measures. An appendix contains suggested projects suitable for end-of-course papers or presentations.

The book is written in a very reader-friendly manner, which makes it appropriate for students of varying degrees of preparation, and the only prerequisite is an undergraduate course in Real Analysis.

• Chapter 3. $L^p$ spaces