Advanced Integration Theory

Corneliu Constantinescu

ISBN 10: 0792352343 / ISBN 13: 9780792352341

Published by Springer Netherlands, Springer Netherlands, 1998

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9780792352341

Bibliographic Details

• Title: Advanced Integration Theory
• Publisher: Springer Netherlands, Springer Netherlands
• Publication Date: 1998
• Language: English
• ISBN 10: 0792352343
• ISBN 13: 9780792352341
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 53D millimeters 241 millimeters width by 160 millimeters height by 53 millimeters depth
• Weight: 1472 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.