Table of Contents

Integration on compact intervals: Gauges and integrals Some examples Basic properties of the integral The fundamental theorems of calculus The Saks-Henstock lemma Measurable functions Absolute integrability Convergence theorems Integrability and mean convergence Measure, measurability, and multipliers Modes of convergence Applications to calculus Substitution theorems Absolute continuity Integration on infinite intervals: Introduction to Part 2 Infinite intervals Further re-examination Measurable sets Measurable functions Sequences of functions Limits superior and inferior Unbounded sets and sequences The arctangent lemma Outer measure Lebesgue's differentiation theorem Vector spaces Semimetric spaces Riemann-Stieltjes integral Normed linear spaces Some partial solutions References Index Symbol index.

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"A comprehensive, beautifully written exposition." Zentralblatt MATH