The Riemann Approach to Integration: Local Geometric Theory (Cambridge Tracts in Mathematics)

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. If E is a set and II is a property of the elements of E, we denote by {x E : II(x)} the set of all elements of E that have the property II.

A detailed exposition of generalised Riemann-Stieltjes integrals.