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N� de ref. del art�culo 1470421992-11-1

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Detalles bibliogr�ficos

T�tulo

A User-friendly Introduction to Lebesgue Measure and Integration (Student Mathematical Library) (Student Mathematical Library, 78)

Editor

American Mathematical Society (edition )

Fecha de publicaci�n

2015

Idioma

Ingl�s

ISBN 10

1470421992

ISBN 13

9781470421991

Encuadernaci�n

Paperback

Estado

Good

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Sinopsis

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.

Acerca del autor

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

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