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Synopsis
This book presents a detailed and mostly elementary exposition of the generalised 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. Defining the Lebesgue integral in Euclidean spaces from the McShane point of view has a clear pedagogical advantage: the initial stages of development are both conceptually and technically simpler. The McShane integral evolves naturally from the initial ideas about integration taught in basic calculus courses. The difficult transition from subdividing the domain to subdividing the range, intrinsic to the Lebeque definition, is completely bypassed. The unintuitive Caratheodory concept of measurability is also made more palatable by means of locally fine partitions. 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.
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Présentation de l'éditeur
This book presents a detailed and mostly elementary exposition of the generalised 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. Defining the Lebesgue integral in Euclidean spaces from the McShane point of view has a clear pedagogical advantage: the initial stages of development are both conceptually and technically simpler. The McShane integral evolves naturally from the initial ideas about integration taught in basic calculus courses. The difficult transition from subdividing the domain to subdividing the range, intrinsic to the Lebeque definition, is completely bypassed. The unintuitive Caratheodory concept of measurability is also made more palatable by means of locally fine partitions. 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.
Revue de presse
"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
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The Riemann Approach to Integration : Local Geometric Theory
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Cambridge University Press, 1994
ISBN 10 : 0521440351
ISBN 13 : 9780521440356
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The Riemann Approach to Integration: Local Geometric Theory
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Cambridge University Press, 1994
ISBN 10 : 0521440351
ISBN 13 : 9780521440356
Ancien ou d'occasion
Couverture rigide
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The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics, Series Number 109)
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ISBN 10 : 0521440351
ISBN 13 : 9780521440356
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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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The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics 109)
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The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics, 109)
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The Riemann approach to integration local geometric theory Washek F. Pfeffer. Cambridge tracts in mathematics and mathematical physics 109; Cambridge tracts in mathematics 109.
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THE RIEMANN APPROACH TO INTEGRATION; LOCAL GEOMETRIC THEORY. Cambridge University Press - Cambridge Tracts in Mathematics #109.
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The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics 109)
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ISBN 10 : 0521440351
ISBN 13 : 9780521440356
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