ENGLISH

The Integrals of Lebesgue, Denjoy, Perron, and Henstock

By Russell A. Gordon

Book information

Publisher
American Mathematical Society
Year
1994
ISBN
0821838059, 9780821838051
Language
english
Format
PDF
Filesize
5 MB (5259229 bytes)
Series
Graduate Studies in Mathematics, Vol.4
Pages
C+xi+395+B\410
DPI
600
Orientation
portrait
Paginated
yes
Scanned
yes
Time added
2014-02-16 10:21:28

Description

This book provides an elementary, self-contained 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 ∫baF′=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 first-year graduate students who have background in real analysis. Readership: First year graduate students in mathematics.

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