A Primer of Lebesgue Integration

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

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