Introduction to Gauge Integrals

By: Charles W. Swartz

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Hardcover | 1 December 2000

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168 Pages

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22.86 x 15.24 x 1.27

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This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces.

A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc.

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Preface
Introduction to the Gauge or Henstock-Kurzweil Integral	p. 1
Basic Properties of the Gauge Integral	p. 13
Henstock's Lemma and Improper Integrals	p. 23
The Gauge Integral over Unbounded Intervals	p. 33
Convergence Theorems	p. 49
Integration over More General Sets: Lebesgue Measure	p. 63
The Space of Gauge Integrable Functions	p. 73
Multiple Integrals and Fubini's Theorem	p. 81
The McShane Integral	p. 99
McShane Integrability is Equivalent to Absolute Henstock-Kurzweil Integrability	p. 121
The Riemann Integral	p. 127
Functions of Bounded Variations	p. 129
Differentiating Indefinite Integrals	p. 135
Equivalence of Lebesgue and McShane Integrals	p. 137
Change of Variable in Multiple Integrals	p. 141
Bibliography	p. 149
Index	p. 155
Table of Contents provided by Blackwell. All Rights Reserved.

Introduction to Gauge Integrals

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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