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## A Modern Theory of Integration (Hardback)"The purpose of this monograph is to present an exposition of a relatively new theory of the integral (variously called the 'generalized Riemann integral', the 'gauge integral', the 'Henstock-Kurzweil integral', etc.) that corrects the defects of the classical Reimann theory and both simplifies and extends the Lebesgue theory of integration." — From the Preface (page ix) ## $19.59 |

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Please contact us if you've got questions about this product.## Condition

**VERY GOOD:** The book is in very good condition, with straight corners and writing-free pages. There is some slight foxing on the top edge. The book was printed on acid-free paper.

## Description

This is volume 32 in the American Mathematical Society’s **Graduate Studies in Mathematics** series.

From the Preface: “Not withing to tell only the easy part of the story, we give here a complete exposition of a theory of integration, initiated around 1960 by Jaroslav Kurzweil and Ralph Henstock. Although much of this theory is at the level of an undergraduate course in real analysis, we are aware that some of the more subtle aspects go slightly beyond that level. Hence this monograph is probably most suitable as a text in a first-year graduate course, although much of it can be readily mastered by less advanced students, or a teacher may simply skip over certain proofs.”

**BRIEF CONTENTS**

- Preface
- Part 1. Integration 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
- Part 2. Integration on infinite intervals
- Introduction to Part 2
- Infinite intervals
- Further re-examination
- Measurable sets
- Measurable functions
- Sequences of functions
- Appendixes
- Limits superior and inferior
- Unbounded sets and sequences
- The arctangent lemma
- Outer measure
- Lebesgue’s differentiation theorem
- Vector spaces
- Semimetric spaces
- The Riemann-Stieltjes integral
- Normed linear spaces
- Some partial solutions
- References
- Index
- Symbol Index

## Details

- SKU:
- 2040
- Subject:
- Mathematics
- Author:
- Bartle, Robert G.
- Publisher:
- American Mathematical Society
- Publish Date:
- 2001 (First Printing)
- Format:
- Hardback
- Weight (pounds):
- 2.28
- Dimensions (W”xL”xH”):
- 7.2″x10.3″x1.1″
- ISBN-13:
- 9780821808450
- ISBN-10:
- 0821808451
- Grade Level:
- Graduate
- Series:
- Graduate Studies in Mathematics

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