**Student Mathematical Library**

Volume: 78;
2015;
221 pp;
Softcover

MSC: Primary 26; 28;

**Print 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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#### Supplemental Materials

# A User-Friendly Introduction to Lebesgue Measure and Integration

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*Gail S. Nelson*

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.

#### Readership

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

#### Table of Contents

# Table of Contents

## A User-Friendly Introduction to Lebesgue Measure and Integration

- Cover Cover11
- Title page i2
- Contents v6
- Preface vii8
- Chapter 0. Review of Riemann integration 112
- Chapter 1. Lebesgue measure 1526
- Chapter 2. Lebesgue integration 5768
- Chapter 3. 𝐿^{𝑝} spaces 107118
- Chapter 4. General measure theory 153164
- Ideas for projects 209220
- References 217228
- Index 219230
- Back Cover Back Cover1233