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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.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
- ÉditeurWspc
- Date d'édition1990
- ISBN 10 9810201451
- ISBN 13 9789810201456
- ReliureBroché
- Langueanglais
- Nombre de pages158
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Concise Introduction To The Theory Of Integration, A (Series in Pure Mathematics)
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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
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A Concise Introduction to the Theory of Integration (Hardback or Cased Book)
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Concise Introduction to the Theory of Integration
Edité par
Wspc, 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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Concise Introduction To The Theory Of Integration, A
Edité par
World Scientific Publishing Company, 1990
ISBN 10 : 9810201451
ISBN 13 : 9789810201456
Neuf
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Concise Intro to the Theory Of. (V12)
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World Scientific Publishing Company, 1990
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Concise Introduction To The Theory Of Integration, A (Hardcover)
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ISBN 10 : 9810201451
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Hardcover. Etat : new. Hardcover. 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 HOELDER are presented. Finally, Chapter VI starts with the DANIELL integral and its applications to the CARATHEODORY Extension and RIESZ Representation Theorems. It closes with VON NEUMANN's derivation of the RADON-NIKODYM Theorem. "The get-up and printing are inviting. This text is designed for a semester course at graduate level." K Chandrasekhara Rao Mathematics Abstracts, 1992 "This book, unusual in many respects, fully achieves its goal, a one-semester, concise but logically complete treatment of abstract integration. There are only 148 pages, making the book psychologically attractive and a price of $18 ." R B Burckel Mathematical Reviews Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9789810201456
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Concise Introduction To The Theory Of Integration, A (Series In Pure Mathematics)
Edité par
Wspc, 1990
ISBN 10 : 9810201451
ISBN 13 : 9789810201456
Ancien ou d'occasion
Couverture rigide
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