The Riemann Approach to Integration: Local Geometric Theory (Paperback)

Washek F. Pfeffer

ISBN 10: 0521056829 / ISBN 13: 9780521056823

Published by Cambridge University Press, Cambridge, 2009

About this Item

Paperback. 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. A detailed exposition of generalised Riemann Stieltjes integrals. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9780521056823

Bibliographic Details

• Title: The Riemann Approach to Integration: Local Geometric Theory (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2009
• Language: English
• ISBN 10: 0521056829
• ISBN 13: 9780521056823
• Binding: Paperback
• Condition: new

About this title

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.

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.