A User-Friendly Introduction to Lebesgue Measure and Integration by Gail S Nelson

A User-Friendly Introduction to Lebesgue Measure and Integration by 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.

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

SKU	Nicht verfügbar
ISBN 13	9781470421991
ISBN 10	1470421992
Titel	A User-Friendly Introduction to Lebesgue Measure and Integration
Autor	Gail S Nelson
Serie	Student Mathematical Library
Buchzustand	Nicht verfügbar
Bindungsart	Paperback
Verlag	American Mathematical Society
Erscheinungsjahr	2015-12-30
Seitenanzahl	221
Hinweis auf dem Einband	Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.
Hinweis	Nicht verfügbar