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Measure and Integration: An Advanced Course in Basic Procedures and Applications

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Synopses & Reviews

Publisher Comments:

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.  

Synopsis:

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.

Synopsis:

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.

Product Details

ISBN:
9783540618584
Author:
Konig, Heinz
Publisher:
Springer
Author:
Konig, Heinz
Author:
Kanig, Heinz
Author:
Knig, Heinz
Author:
K??nig, Heinz
Subject:
Calculus
Subject:
Mathematical Analysis
Subject:
Measure theory
Subject:
Functional Analysis
Subject:
Integrals, generalized
Subject:
measure
Subject:
capacity
Subject:
construction of measures
Subject:
integral representation
Subject:
Mathematics-Calculus
Subject:
Real functions
Copyright:
Edition Number:
1
Edition Description:
1996. Corr. 2nd
Publication Date:
20111114
Binding:
HARDCOVER
Language:
English
Pages:
282
Dimensions:
235 x 155 mm 1290 gr

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Related Subjects

Science and Mathematics » Chemistry » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Functional Analysis

Measure and Integration: An Advanced Course in Basic Procedures and Applications New Hardcover
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Product details 282 pages Springer - English 9783540618584 Reviews:
"Synopsis" by , 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.
"Synopsis" by , 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.
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