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A Primer of Lebesgue Integration

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A Primer of Lebesgue Integration

H. Bear

ISBN 0120839717
Pages 164

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.

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 and General Measures; Integration for General Measures; More Integration: The Radon-Nikodym Theorem; Product Measures; The Space L2; Index