This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem. The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory. The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course.
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Professor Heinz Bauer (1928--2002) was Professor at the Mathematical Institute of the Friedrich-Alexander-University Erlangen-Nürnberg, Erlangen, Germany.
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Hardback. Zustand: New. 1. The series De Gruyter Studies in Mathematics was founded in 1982 by the late Professor Heinz Bauer and Professor Peter Gabriel. The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series De Gruyter Studies in Mathematics is indexed in MathSciNet (Mathematical Reviews) and Scopus. Editor-in-Chief Guozhen Lu, University of Connecticut, USA Editorial Board Carstensen Carsten, Humboldt-Universitat zu Berlin, Germany Gavril Farkas, Humboldt-Universitat zu Berlin, Germany Nicola Fusco, Università di Napoli "Federico II", Italy Fritz Gesztesy, Baylor University, USA Zenghu Li, Beijing Normal University, China Karl-Hermann Neeb, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany René L. Schilling, Technische Universität Dresden, Germany Volkmar Welker, Philipps-Universität Marburg, Germany Please submit book proposals to Guozhen Lu. Artikel-Nr. LU-9783110167191
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Hardback. Zustand: New. 1. The series De Gruyter Studies in Mathematics was founded in 1982 by the late Professor Heinz Bauer and Professor Peter Gabriel. The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series De Gruyter Studies in Mathematics is indexed in MathSciNet (Mathematical Reviews) and Scopus. Editor-in-Chief Guozhen Lu, University of Connecticut, USA Editorial Board Carstensen Carsten, Humboldt-Universitat zu Berlin, Germany Gavril Farkas, Humboldt-Universitat zu Berlin, Germany Nicola Fusco, Università di Napoli "Federico II", Italy Fritz Gesztesy, Baylor University, USA Zenghu Li, Beijing Normal University, China Karl-Hermann Neeb, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany René L. Schilling, Technische Universität Dresden, Germany Volkmar Welker, Philipps-Universität Marburg, Germany Please submit book proposals to Guozhen Lu. Artikel-Nr. LU-9783110167191
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on 'Probability Theory and Measure Theory'. Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem. The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory. The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course. Artikel-Nr. 9783110167191
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