Measure and Integration

Name: Measure and Integration
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783642082771
Price: 52.71 EUR
Availability: InStock

An Advanced Course in Basic Procedures and Applications

Автор: Heinz König

Език:

Корици: С меки корици

Издател: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Наличност: Външен склад

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52.71 € 103.09 лв

This book aims at restructuring some fundamentals in measure and integration theory. It centers arou...

Информация за книгата

Автор

Heinz König

Език

Английски език

Корици

Книга - С меки корици

Издадена

2010

страници

260

EAN

9783642082771

ISBN

3642082777

Enbook ID

01653306

Издател

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Теглоt

439

Размери

155 x 235 x 16

Пълно описание

This book aims at restructuring some fundamentals in measure and integration theory. It centers around the ubiquitous task to produce appropriate contents and measures from more primitive data like elementary contents and elementary integrals. It develops the new approach started around 1970 by Topsoe and others into a systematic theory. The theory is much more powerful than the traditional means and has striking implications all over measure theory and beyond.This book sets out to restructure certain fundamentals in measure and integration theory, and thus to fee the theory from some notorious drawbacks. It centers around the ubiquitous task of producing appropriate contents and measures from more primitive data, in order to extend elementary contents and to represent elementary integrals. This task has not been met with adequate unified means so far. The traditional main tools, the Carathéodory and Daniell-Stone theorems, are too restrictive and had to be supplemented by other ad-hoc procedures. Around 1970 a new approach emerged, based on the notion of regularity, which in traditional measure theory is linked to topology. The present book develops the new approach into a systematic theory. The theory unifies the entire context and is much more powerful than the former means. It has striking implications all over measure theory and beyond. Thus it extends the Riesz representation theorem in terms of Randon measures from locally compact to arbitrary Hausdorff topological spaces. It furthers the methodical unification with non-additive set functions, as shown in natural extensions of the Choquet capacitability theorem. The presentation of this research monograph is self-contained, and starts from the beginning. It is addressed to research workers in mathematical analysis and in applications like mathematical economics, and in particular for university teachers in measure and integration theory. The corrected, second printing includes required corrections and appropriate small alterations of the text and a list of the subsequent articles by the author.

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Measure and Integration

An Advanced Course in Basic Procedures and Applications

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