Graduate Studies in Mathematics 1994; 395 pp; hardcover Volume: 4 Reprint/Revision History: reprinted with corrections 1997 ISBN10: 0821838059 ISBN13: 9780821838051 List Price: US$53 Member Price: US$42.40 Order Code: GSM/4
 This book provides an elementary, selfcontained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus: if \(F\) is differentiable on the interval \([a,b]\), then \(F'\) is integrable on \([a,b]\) and \(\int _a^b F'= F(b)  F(a)\). One of the book's unique features is that the Denjoy, Perron, and Henstock integrals are each developed fully and carefully from their corresponding definitions. The last part of the book is devoted to integration processes which satisfy a theorem analogous to the Fundamental Theorem, in which \(F\) is approximately differentiable. This part of this book is preceded by a detailed study of the approximate derivative and ends with some open questions. This book contains over 230 exercises (with solutions) that illustrate and expand the material in the text. It would be an excellent textbook for firstyear graduate students who have background in real analysis. Readership First year graduate students in mathematics. Table of Contents  Lebesgue measure
 Measurable functions
 The Lebesgue integral
 Bounded variation and absolute continuity
 Darboux and Baire class one functions
 Functions of generalized bounded variation
 The Denjoy integral
 The Perron integral
 The Henstock integral
 The McShane integral
 Equivalence of integrals
 Integration by parts
 Convergence theorems
 Approximate derivatives
 The Khintchine integral
 The approximately continuous Henstock integral
 The approximately continuous Perron integral
 Solutions to exercises
 References
 Notation index
 Subject index
