Overview

In this chapter we shall present the theory of integration introduced by the contemporary Czech mathematician J.Kurzweil. Sometimes it is referred to as Kurzweil-Henstock ^[1] theory. The first modern integration theory was developed by the German mathematician B.Riemann. His definition of an integral was similar but more innovative than the one developed previously by A.L.Cauchy. Riemann made a decisive steps forward by considering the totality of functions which can be integrated and building a systematic theory. Initially Riemann s theory was a great success. Later it was found deficient in many aspects. However, unfortunate as it may be, it is this theory which is usually presented to first year classes and dealt with in books on calculus. Our presentation follows, in parts, Lee and V born (2000, Chapter 2). ^[2]