Description
Book SynopsisGives an introduction to the theory of the integral (called the 'generalized Riemann integral' or the 'Henstock-Kurzweil integral') that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration. This book includes a study of measure theory as an application of the integral.
Trade ReviewA comprehensive, beautifully written exposition. Zentralblatt MATH
Table of ContentsIntegration 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.
