A User-Friendly Introduction to Lebesgue Measure and Integration

Gail S. Nelson

ISBN 10: 1470421992 / ISBN 13: 9781470421991

Verlag: American Mathematical Society, 2015

Beschreibung

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. Series: Student Mathematical Library. Num Pages: 221 pages, illustrations. BIC Classification: PBK. Category: (G) General (US: Trade). Dimension: 143 x 216 x 15. Weight in Grams: 270. . 2015. Paperback. . . . . Books ship from the US and Ireland.

Bestandsnummer des Verkäufers V9781470421991

Bibliografische Details

• Titel: A User-Friendly Introduction to Lebesgue Measure and Integration
• Verlag: American Mathematical Society
• Erscheinungsjahr: 2015
• Sprache: Englisch
• ISBN-10: 1470421992
• ISBN-13: 9781470421991
• Einband: Softcover
• Zustand: New

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

Gail S. Nelson, Carleton College, Northfield, MN, USA.