Henstock Ralph. The Calculus and Gauge Integrals

ArXiv, 2016. — 80 p.Ralph Henstock (1923 - 2007), with (independently) Jaroslav Kurzweil, was the originator of the Riemann-complete or generalized Riemann integral. This material consists of four chapters of a book proposal to Cambridge University Press, which remained unpublished in the Henstock Archive at the University of Ulster. Section 5 presents a novel approach to taking limits under the integral sign, and goes on to place the traditional monotone and dominated convergence theorems of Lebesgue in this new context.The Calculus.
Simple Definite Integration.
Gauge Integration.
Limits Under the Integral Sign.