Introduction -- Preliminaries concerning semi-groups and limits -- Notation and definitions -- Elementary properties -- Henstock's lemma -- Absolute integrability -- The monotone convergence theorem -- The dominated convergence theorem -- A more traditional type of integral -- Convergence theorems -- Measure -- Examples : integrals of Stieltjes type -- Examples -- The Bochner, Pettis and Bogdanowicz integrals -- Stochastic integrals
Summary
One of the difficulties with integration theory is that there are so many different detailed definitions that the non-expert is confused about their relative strengths and usefulness. A surprising recent development in the theory of integration has been the discovery that suitable modifications to the Riemann definition using approximating sums can produce a wide variety of different integrals including integrals of great power
