書誌事項

Advanced integration theory

by Corneliu Constantinescu ... [et al.]

(Mathematics and its applications, v. 454)

Kluwer Academic Publishers, c1998

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注記

Includes indexes

内容説明・目次

内容説明

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.

目次

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.

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