Introduction to Gauge Integrals,9789810242398

Introduction to Gauge Integrals

by
ISBN13: 9789810242398
ISBN10: 9810242395
Format: Hardcover
Pub. Date: 2001-07-01
Publisher(s): WORLD SCIENTIFIC PUB CO INC
List Price: $71.00

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Summary

A presentation of the Henstock/Kurzweil integral and the McShane integral, explaining how these are obtained and why they can lead to more powerful integrals than the Riemann integral. Requires a basic knowledge of real analysis, conversion, real numbers, series, differentiation and continuity. DLC: Gauge integrals.

Table of Contents

Preface v
Introduction to the Gauge or Henstock-Kurzweil Integral
1(12)
Basic Properties of the Gauge Integral
13(10)
Henstock's Lemma and Improper Integrals
23(10)
The Gauge Integral over Unbounded Intervals
33(16)
Convergence Theorems
49(14)
Integration over More General Sets: Lebesgue Measure
63(10)
The Space of Gauge Integrable Functions
73(8)
Multiple Integrals and Fubini's Theorem
81(18)
The McShane Integral
99(22)
Definition and Basic Properties
99(6)
Convergence Theorems
105(5)
Integrability of Products and Integration by Parts
110(2)
More General Convergence Theorems
112(3)
The Space of McShane Integrable Functions
115(1)
Multiple Integrals and Fubini's Theorem
116(5)
McShane Integrability is Equivalent to Absolute Henstock-Kurzweil Integrability
121(6)
Appendix 1: The Riemann Integral 127(2)
Appendix 2: Functions of Bounded Variations 129(6)
Appendix 3: Differentiating Indefinite Integrals 135(2)
Appendix 4: Equivalence of Lebesgue and McShane Integrals 137(4)
Appendix 5: Change of Variable in Multiple Integrals 141(8)
Bibliography 149(6)
Index 155

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