Since about 1915 integration theory has consisted of two separate branches: the abstract theory required by probabilists and the theory, preferred by analysts, that combines integration and topology. As long as the underlying topological space is reasonably nice (e.g., locally compact with countable basis) the abstract theory and the topological theory yield the same results, but for more compli cated spaces the topological theory gives stronger results than those provided by the abstract theory. The possibility of resolving this split fascinated us, and it was one of the reasons for writing this book. The unification of the abstract theory and the topological theory is achieved by using new definitions in the abstract theory. The integral in this book is de fined in such a way that it coincides in the case of Radon measures on Hausdorff spaces with the usual definition in the literature. As a consequence, our integral can differ in the classical case. Our integral, however, is more inclusive. It was defined in the book "C. Constantinescu and K. Weber (in collaboration with A.
Authors and Affiliations
Department of Mathematics, ETH-Zürich, Zürich, Switzerland
Corneliu Constantinescu
Department of Mathematics, Faculty of Engineering, Università di Palermo, Palermo, Italy
Wolfgang Filter
Technikum Winterthur, Winterthur, Switzerland
Karl Weber
Department of Mathematics, Wellesley College, Wellesley, USA
Alexia Sontag
Bibliographic Information
Book Title: Advanced Integration Theory
Authors: Corneliu Constantinescu, Wolfgang Filter, Karl Weber, Alexia Sontag
