A Primer of Lebesgue Integration

A Primer of Lebesgue Integration

2nd Edition - September 17, 2001

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  • Author: H. Bear
  • eBook ISBN: 9780080525730

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The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study. Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels.


Advanced undergraduate and beginning graduate students in mathematics

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

Product details

  • No. of pages: 164
  • Language: English
  • Copyright: © Academic Press 2001
  • Published: September 17, 2001
  • Imprint: Academic Press
  • eBook ISBN: 9780080525730

About the Author

H. Bear

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.

Affiliations and Expertise

University of Hawaii at Manoa, Honolulu, U.S.A.

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