A comprehensive review of the Kurzweil-Henstock integration process on the real line and in higher dimensions. It seeks to provide a unified theory of integration that highlights Riemann-Stieljes and Lebesgue integrals as well as integrals of elementary calculus. The author presents practical applications of the definitions and theorems in each section as well as appended sets of exercises.
Table of Contents
Integration of summants; differentials and their integrals; differentials with special properties; measurable sets and functions; the Vitali covering theorem applied to differentials; derivatives and differentials; essential properties of functions; absolute continuity; conversion of Lebesgue-Stieljes integrals into Lebesgue integrals; some results on higher dimensions.