ABSTRACT

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 sec

chapter |4 pages

§0.1 The Gauge-Directed Integral

chapter |1 pages

§0.2 Differentials

chapter |3 pages

§0.3 Guidance for the Reader

chapter |6 pages

over a Figure

chapter |8 pages

§1.4 Summants with Special Properties

chapter |4 pages

Boolean Algebra of Figures

chapter |2 pages

tion

chapter |2 pages

on K

chapter |6 pages

ferentials

chapter |9 pages

orems

chapter |9 pages

Differentials

chapter |3 pages

§3.2 Continuous Differentials

chapter |5 pages

Functions

chapter |4 pages

§3.7 n-Differentials on a Cell K

chapter |8 pages

§4.3 Measurable Functions

chapter |6 pages

§4.6 Minimal Measurable Dominators

chapter |13 pages

culus

chapter |7 pages

Using Essential Limits

chapter |3 pages

§7.2 Essentially Regulated Functions

chapter |8 pages

§7.3 Essential Variation

chapter |4 pages

Differentials

chapter |4 pages

Differentials

chapter |5 pages

§8.3 Absolutely Continuous Functions

chapter |5 pages

§8.4 The Vitali Convergence Theorem

chapter |3 pages

§9.1 Banach’s Indicatrix Theorem

chapter |15 pages

Applications

chapter |10 pages

§10.2 Direct Products of Summants

chapter |9 pages

§10.4 Integration on Paths in Rn

chapter |7 pages

§10.5 Green’s Theorem