The Riemann Approach to Integration
Local Geometric Theory
By (author) Washek F. Pfeffer
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Riemann Approach to Integration by Washek F. Pfeffer
Book DescriptionThis 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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Book DetailsISBN: 9780521056823
(229mm x 152mm x 18mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 24-Mar-2008
Country of Publication: United Kingdom
Books By Author Washek F. Pfeffer
Derivation and Integration, Paperback (July 2010)
A 2001 treatment of the classical problem of derivation and integration, with applications to the Gauss-Green and Stokes theorems.
Riemann Approach to Integration, Hardback (February 1994)» View all books by Washek F. Pfeffer
A detailed exposition of generalised Riemann-Stieltjes integrals.
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