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A Primer of Lebesgue Integration / Edition 2

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Overview

This successful text offers a reader-friendly approach to Lebesgue integration. It is designed for advanced undergraduates, beginning graduate students, or advanced readers who may have forgotten one or two details from their real analysis courses.

"The Lebesgue integral has been around for almost a century. Most authors prefer to blast through the preliminaries and get quickly to the more interesting results. This very efficient approach puts a great burden on the reader; all the words are there, but none of the music." Bear's goal is to proceed more slowly so the reader can develop some intuition about the subject. Many readers of the successful first edition would agree that he achieves this goal.

The principal change in this edition is the simplified definition of the integral. The integral is defined either with upper and lower sums as in the calculus, or with Riemann sums, but using countable partitions of the domain into measurable sets. This one-shot approach works for bounded or unbounded functions and for sets of finite or infinite measure.

The author's style is graceful and pleasant to read. The explanations are exceptionally clear. Someone looking for an introduction to Lebesgue integration could scarcely do better than this text.

—John Erdman
Portland State University

This is an excellent book. Several features make it unique. The author gets through the standard canon in only 150 pages and then arranges the material into easily digestible units (a proof hardly ever exceeds three-fourths of a page). The author writes with concision, clarity, and focus.

—Robert Burckel
Kansas State University

This text achieves its worthy goals. The author tends to the business at hand. The short chapter on Lebesgue integration is refreshing and easily understood. One can use a semester covering the book, and the students will be well-grounded in the basics and ready for any of a dozen possible second semesters.
—Joseph Diestel
Kent State University

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Editorial Reviews

From the Publisher
"This well-written little book provides ... an introduction to the Lebesgue integral. The book is written very clearly and suggestively and can be recommended to students." Zentralblatt for Mathematik
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Product Details

  • ISBN-13: 9780120839711
  • Publisher: Elsevier Science
  • Publication date: 9/1/2001
  • Edition description: REV
  • Edition number: 2
  • Pages: 164
  • Product dimensions: 0.56 (w) x 6.00 (h) x 9.00 (d)

Meet the Author

H.S. Bear is a professor at the University of Hawaii, Manoa and a member of both the American Mathematical Society and the Mathematical Association of America.
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Table of Contents

The Riemann-Darboux Integral; The Riemann Integral as a Limit of Sums; Lebesgue Measure on (0, 1);
Measurable Sets: The Caratheodory Characterization;
The Lebesgue Integral for Bounded Functions; Properties of the Integral; The Integral of Unbounded Functions; Differentiation and Integration; Plane Measure; The Relationship between µ and General Measures; Integration for General Measures; More Integration: The Radon-Nikodym Theorem; Product Measures; The Space L2; Index
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