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The integrals of Lebesgue, Denjoy, Perron, and Henstock

Author: Russell A Gordon
Publisher: Providence, R.I. : American Mathematical Society, ©1994.
Series: Graduate studies in mathematics, v. 4.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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. The Denjoy, Perron, and Henstock integrals are each  Read more...
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Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Russell A Gordon
ISBN: 0821838059 9780821838051
OCLC Number: 30474120
Description: xi, 395 pages : illustrations ; 27 cm.
Contents: Ch. 1. Lebesgue measure --
Ch. 2. Measurable functions --
Ch. 3. The Lebesgue integral --
Ch. 4. Bounded variation and absolute continuity --
Ch. 5. Darboux and Baire class one functions --
Ch. 6. Functions of generalized bounded variation --
Ch. 7. The Denjoy integral --
Ch. 8. The Perron integral --
Ch. 9. The Henstock integral --
Ch. 10. The McShane integral --
Ch. 11. Equivalence of integrals --
Ch. 12. Integration by parts --
Ch. 13. Convergence theorems --
Ch. 14. Approximate derivatives --
Ch. 15. The Khintchine integral --
Ch. 16. The approximately continuous Henstock integral --
Ch. 17. The approximately continuous Perron integral --
Solutions to exercises.
Series Title: Graduate studies in mathematics, v. 4.
Responsibility: Russell A. Gordon.
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Abstract:

Offers an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. This book contains over 230 exercises (with solutions) that  Read more...

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