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Synopsis
The choice of topics included in this book, as well as the presentation of those topics, has been guided by the author's experience in teaching this material to classes consisting of advanced graduate students who are not concentrating in mathematics. This book contains an introduction to the modern theory of integration with a strong emphasis on the case of Lebesgue's measure for (Rn and eye toward applications to real analysis and probability theory. Following a brief review of the classical Riemann theory in Chapter I, the details of Lebesgue's construction are given in Chapter Ii, which also contains a derivation of the transformation properties of Lebesgue's measure under linear maps. Chapter Iii is devoted to Lebesgue's theory of integration of real-valued functions on a general measure space. Besides the basic convergence theorems, this chapter introduces product measures and Fubini's Theorem. In Chapter Iv, various topics having to do with the transformation properties of measures are derived. These include: the representation of general integrals in terms of Riemann integrals with respect to the distribution function, polar coordinates, Jacobi's transformation formula and finally the introduction of surface measure followed by a proof of the Divergence Theorem. A few of the basic inequalitites of measure theory are derived in Chapter V. In particular, the inequalities of Jensen, Minkowski and HÖLder are presented. Finally, Chapter Vi starts with the Daniell integral and its applications to the CarathÉOdory Extension and Riesz Representation Theorems. It closes with Von Neumann's derivation of the Radon-Nikodym Theorem.
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Présentation de l'éditeur
The choice of topics included in this book, as well as the presentation of those topics, has been guided by the author's experience in teaching this material to classes consisting of advanced graduate students who are not concentrating in mathematics. This book contains an introduction to the modern theory of integration with a strong emphasis on the case of Lebesgue's measure for (Rn and eye toward applications to real analysis and probability theory. Following a brief review of the classical Riemann theory in Chapter I, the details of Lebesgue's construction are given in Chapter Ii, which also contains a derivation of the transformation properties of Lebesgue's measure under linear maps. Chapter Iii is devoted to Lebesgue's theory of integration of real-valued functions on a general measure space. Besides the basic convergence theorems, this chapter introduces product measures and Fubini's Theorem. In Chapter Iv, various topics having to do with the transformation properties of measures are derived. These include: the representation of general integrals in terms of Riemann integrals with respect to the distribution function, polar coordinates, Jacobi's transformation formula and finally the introduction of surface measure followed by a proof of the Divergence Theorem. A few of the basic inequalitites of measure theory are derived in Chapter V. In particular, the inequalities of Jensen, Minkowski and HÖLder are presented. Finally, Chapter Vi starts with the Daniell integral and its applications to the CarathÉOdory Extension and Riesz Representation Theorems. It closes with Von Neumann's derivation of the Radon-Nikodym Theorem.
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A concise introduction to the theory of integration Daniel W. Stroock. Series in pure mathematics 12.
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Singapore New Jersey, World Scientific [1990]., 1990
ISBN 10 : 9810201451
ISBN 13 : 9789810201456
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Concise Introduction To The Theory Of Integration, A (Pure Mathematics)
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A Concise Introduction to the Theory of Integration
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World Scientific Publishing Co Pte Ltd, 1990
ISBN 10 : 9810201451
ISBN 13 : 9789810201456
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Concise Introduction To The Theory Of Integration, A (Series In Pure Mathematics)
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ISBN 13 : 9789810201456
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A Concise Introduction To The Theory Of Integration.
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gebundene Ausgabe. Etat : Sehr gut. Series in Pure Mathematics, Band 12. Zust: Gutes Exemplar. Mit original Schutzumschlag. Schutzumschlag mit Lichtrand und am Buchrücken ausgeblichen. VII, 148 Seiten, Englisch 376g. N° de réf. du vendeur 492041
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Concise Introduction To The Theory Of Integration, A
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ISBN 13 : 9789810201456
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Concise Intro to the Theory Of. (V12)
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World Scientific Publishing Company, 1990
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ISBN 13 : 9789810201456
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Concise Introduction To The Theory Of Integration, A (Pure Mathematics)
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Concise Introduction To The Theory Of Integration, A (Pure Mathematics)
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A Concise Introduction to the Theory of Integration (Hardback or Cased Book)
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