Softcover ISBN:  9781470421991 
Product Code:  STML/78 
List Price:  $52.00 
Individual Price:  $41.60 
Electronic ISBN:  9781470427375 
Product Code:  STML/78.E 
List Price:  $49.00 
Individual Price:  $39.20 

Book DetailsStudent Mathematical LibraryVolume: 78; 2015; 221 ppMSC: Primary 26; 28;
A UserFriendly Introduction to Lebesgue Measure and Integration provides a bridge between an undergraduate course in Real Analysis and a first graduatelevel 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 endofcourse papers or presentations.
The book is written in a very readerfriendly manner, which makes it appropriate for students of varying degrees of preparation, and the only prerequisite is an undergraduate course in Real Analysis.ReadershipUndergraduate and graduate students and researchers interested in learning and teaching real analysis.

Table of Contents

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


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A UserFriendly Introduction to Lebesgue Measure and Integration provides a bridge between an undergraduate course in Real Analysis and a first graduatelevel 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 endofcourse papers or presentations.
The book is written in a very readerfriendly 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