Advanced Integration Theory

Corneliu Constantinescu

ISBN 10: 9401037396 / ISBN 13: 9789401037396

Published by Springer, Springer Dez 2012, 2012

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 884 pp. Englisch.

Seller Inventory # 9789401037396

Bibliographic Details

• Title: Advanced Integration Theory
• Publisher: Springer, Springer Dez 2012
• Publication Date: 2012
• Language: English
• ISBN 10: 9401037396
• ISBN 13: 9789401037396
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 160H x 48D millimeters 240 millimeters width by 160 millimeters height by 48 millimeters depth
• Weight: 1382 grams

About this title

Synopsis

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.