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Advanced Integration Theory
Mathematics and Its Applications 454
ISBN/EAN: 9789401037396
Umbreit-Nr.: 5647389
Sprache:
Englisch
Umfang: xxiv, 876 S., 1 s/w Illustr.
Format in cm:
Einband:
kartoniertes Buch
Erschienen am 21.12.2012
Auflage: 1/1998
- Zusatztext
- 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.