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Measure and integration: an advanced course in basic procedures and applications

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 an...

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Detalles Bibliográficos
Autor principal: König, Heinz
Lenguaje:eng
Publicado: Springer 1997
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-540-89502-2
http://cds.cern.ch/record/2023389
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author König, Heinz
author_facet König, Heinz
author_sort König, Heinz
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description 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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spelling cern-20233892021-04-21T20:13:36Zdoi:10.1007/978-3-540-89502-2http://cds.cern.ch/record/2023389engKönig, HeinzMeasure and integration: an advanced course in basic procedures and applicationsMathematical Physics and MathematicsThis 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. .Springeroai:cds.cern.ch:20233891997
spellingShingle Mathematical Physics and Mathematics
König, Heinz
Measure and integration: an advanced course in basic procedures and applications
title Measure and integration: an advanced course in basic procedures and applications
title_full Measure and integration: an advanced course in basic procedures and applications
title_fullStr Measure and integration: an advanced course in basic procedures and applications
title_full_unstemmed Measure and integration: an advanced course in basic procedures and applications
title_short Measure and integration: an advanced course in basic procedures and applications
title_sort measure and integration: an advanced course in basic procedures and applications
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-540-89502-2
http://cds.cern.ch/record/2023389
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