Integration Between the Lebesgue Integral and the Henstock-Kurzweil Integral: Its Relation to Local Convex Vector Spaces

Description

The main topics of this book are convergence and topologization. Integration on a compact interval on the real line is treated with Riemannian sums for various integration bases. General results are specified to a spectrum of integrations, including Lebesgue integration, the Denjoy integration in the restricted sense, the integrations introduced by Pfeffer and by Bongiorno, and many others. Morever, some relations between integration and differentiation are made clear.The book is self-contained. It is of interest to specialists in the field of real functions, and it can also be read by students, since only the basics of mathematical analysis and vector spaces are required Content: Contents: Basic Concepts and Properties of y-Integration Convergence Convergence and Locally Convex Spaces An Auxiliary Locally Convex Space L-Integration M-Integration Noncompleteness S-Integration R-Integration An Extension of the Concept of y-Integration Differentiation and Integration.