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The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics, Series Number 109) - Hardcover
Synopsis
This book presents a detailed and mostly elementary exposition of the generalized Riemann-Stieltjes integrals discovered by Henstock, Kurzweil, and McShane. Along with the classical results, it contains some recent developments connected with lipeomorphic change of variables and the divergence theorem for discontinuously differentiable vector fields.
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Book Description
This book presents a detailed and mostly elementary exposition of the generalised Riemann-Stieltjes integrals discovered by Henstock, Kurzweil, and McShane more than thirty years ago. Aside from classical results, it contains some recent developments connected with lipeomorphic change of variable and the divergence theorem for discontinuously differentiable vector fields.
Review
"The author presents a detailed exposition of some recent (Riemann!) approaches to generalized integrals of real-valued functions on compact intervals in Euclidean spaces Rm (m>=1)...The author presents this theory in a very complete, thorough manner." R.G. Bartle, Mathematical Reviews
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The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics, Series Number 109)
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Cambridge University Press, 1994
ISBN 10: 0521440351
ISBN 13: 9780521440356
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Hardcover
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The Riemann Approach to Integration: Local Geometric Theory
Published by
Cambridge University Press, 1994
ISBN 10: 0521440351
ISBN 13: 9780521440356
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Hardcover
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hardcover. Condition: Acceptable. May have underlining, highlighting, margin notes, remainder marks, inscriptions, book plates, tears, significant wear, and/or a missing dust jacket, box, or discs. Damaged item. Seller Inventory # 1486790
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The Riemann Approach to Integration: Local Geometric Theory
Published by
Cambridge University Press, 1994
ISBN 10: 0521440351
ISBN 13: 9780521440356
Used
Hardcover
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Hardcover. Condition: Very Good. No Jacket. Former library book; May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend Less. Seller Inventory # G0521440351I4N10
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The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics, Series Number 109)
Published by
Cambridge University Press, 1994
ISBN 10: 0521440351
ISBN 13: 9780521440356
Used
Hardcover
Seller: Friends of Pima County Public Library, Tucson, AZ, U.S.A.
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hardcover. Condition: Good. Hardcover. NOT Ex-library. Notes, Bibliography, Index. This item is in good condition. May show moderate signs of use. Until further notice, USPS Priority Mail only reliable option for Hawaii. Proceeds benefit the Pima County Public Library system, which serves Tucson and southern Arizona. Seller Inventory # 529WDE000GZL
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The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics 109)
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Cambridge University Press, c.1993,, 1993
ISBN 10: 0521440351
ISBN 13: 9780521440356
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hardcover, Condition: Very Good, Cambridge University Press, c.1993, 1st., 8vo., cloth, (xv,302)pp., VG in rubbed & sunned dj $. Seller Inventory # 90896
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The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics, 109)
Published by
Cambridge University Press, Cambridge, England, 1993
ISBN 10: 0521440351
ISBN 13: 9780521440356
Used
Hardcover
First Edition
Seller: Fahrenheit's Books, Denver, CO, U.S.A.
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Hardcover. Condition: Very Good. Dust Jacket Condition: Very Good. 1st Edition. First edition, hardcover, has a slight lean to binding, very faint bowing to boards, a touch of shelfwear to spine ends and corners, and previous owner's small note to top of first endpage, otherwise a solid VG copy in like dust jacket which has slight bumps to spine ends and corners with a tiny tear to top of spine, some rubbing, very slight edgewear, and faint sunning to spine. Seller Inventory # 98093
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The Riemann Approach to Integration: Local Geometric Theory
Published by
Cambridge University Press, 1993
ISBN 10: 0521440351
ISBN 13: 9780521440356
Used
Hardcover
Seller: Epilonian Books, Manhattan Beach, CA, U.S.A.
Seller rating 5 out of 5 stars
Hardcover. Condition: Very Good. Dust Jacket Condition: Good. Cambridge University Press, Published 1993. Hardcover, 302 pp.; 24 cm; First Edition. In Very Good condition with a Good dust jacket. Dark blue cloth boards, silver lettering on spine, mild shelf and edge wear with some color loss along edges and spine hinges. Binding tight. Pages clean and unmarked, a few small spots to rear endpaper. Light blue dust jacket, several nicks and closed tears of half an inch or less, creasing along edges and at flap folds, some soiling, and a semi-circular stain to paper over top edge of front cover near corner. Otherwise unmarked. Now in an archival quality (removable) Brodart cover. Number 109 in Cambridge Tracts in Mathematics, a series of single-thread monographs intended as definitive treatments. [From front flap] This book presents a detailed and mostly elementary exposition of the generalized Riemann integrals discovered by Henstock, Kurzweil, and McShane. Along with the classical results, it contains some recent developments connected with lipeomorphic change of variables, higher dimensional multipliers, and the divergence theorem for discontinuously differentiable vector fields. Defining the Lebesgue integral in Euclidean spaces from McShane's point of view has a clear pedagogical advantage, since the initial stages of development are both conceptually and technically simpler. The McShane integral evolves directly from the basic ideas about integration taught in elementary calculus. The difficult transition from subdividing the domain to subdividing the range, intrinsic to the Lebesgue definition, is completely bypassed. The unintuitive Caratheodory concept of measurability is also made more palatable by means of locally fine partitions. The mathematical significance of the generalized Riemann integrals emerges when the Henstock-Kurzweil approach is used to define the Denjoy-Perron integral. While there is little similarity between the classical definitions of Lebesgue, Denjoy, and Perron, the Lebesgue and Denjoy-Perron integrals are naturally connected via the McShane and Henstock-Kurzweil definitions. This is used to obtain a coordinate free multidimensional integral which provides an unrestricted Gauss-Green theorem for vector fields with large sets of singularities. Although written as a monograph, the book can be used as a graduate text, and certain portions of it can be presented even to advanced undergraduate students with a working knowledge of limits, continuity, and differentiation on the real line. Contents: Preface; Acknowledgments; One-dimensional integration: Preliminaries, The McShane integral, Measure and measurability, Integrable functions, Descriptive definition, The Henstock-Kurzweil integral; Multidimensional integration: Preliminaries, The McShane integral, Descriptive definition, Change of variables, The gage integral, The F-integral, Recent developments; Bibliography; List of symbols; Index. Seller Inventory # 20260915012
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The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics 109)
Published by
Cambridge University Press, Cambridge, 1993
ISBN 10: 0521440351
ISBN 13: 9780521440356
Used
Hardcover
First Edition
Seller: Literary Cat Books, Machynlleth, Powys, WALES, United Kingdom
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Original cloth. Condition: Very Good. Dust Jacket Condition: Very Good-. First Edition. Minor annotation on front free endpaper. Slight wear to spine, covers & corners. Dustjacket somewhat worn & slightly soiled.; Octavo; xvi, 306 pages. Seller Inventory # LCB61535
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THE RIEMANN APPROACH TO INTEGRATION; LOCAL GEOMETRIC THEORY. Cambridge University Press - Cambridge Tracts in Mathematics #109.
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Cambridge [England], New York, Melbourne: Cambridge University Press, 1993., 1994
ISBN 10: 0521440351
ISBN 13: 9780521440356
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Hardcover
First Edition
Seller: David Hallinan, Bookseller, Columbus, MS, U.S.A.
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First edition (per publisher's statement upon copyright page). xvi, 302 pages. Hardcover: H 23.5cm x L 15.5cm. Light blue dust jacket rubbed. Dark blue cloth with vibrant gilt stamped spine lettering. Interior pages are bright and clean. Binding is firm. A near fine copy in a very good+ dust jacket. ISBN 0521440351. Seller Inventory # Z626X-3170
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The Riemann Approach to Integration: Local Geometric Theory
Published by
Cambridge University Press, 1994
ISBN 10: 0521440351
ISBN 13: 9780521440356
Used
Hardcover
First Edition
Seller: mathbooks, Tallahassee, FL, U.S.A.
Seller rating 5 out of 5 stars
Hardcover. Condition: As New. Dust Jacket Condition: Very Good. 1st Edition. 302 pages. Unmarked. Fine. Seller Inventory # 356