Advanced Integration Theory by Corneliu ConstantinescuAdvanced Integration Theory by Corneliu Constantinescu

Advanced Integration Theory

byCorneliu Constantinescu, Wolfgang Filter, Karl Weber

Paperback | December 21, 2012

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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.
Title:Advanced Integration TheoryFormat:PaperbackDimensions:876 pagesPublished:December 21, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401037396

ISBN - 13:9789401037396

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Table of Contents

Preface. Introduction. Suggestions to the Reader. 0. Preliminaries. 1. Vector Lattices. 2. Elementary Integration Theory. 3. Lp-Spaces. 4. Real Measures. 5. The Radon-Nikodym Theorem Duality. 6. The Classical Theory of Real Functions. Historical Remarks. Name Index. Subject Index. Symbol Index.