Real Analysis - Couverture souple

Loeb, Peter A.

Couverture souple

ISBN 10 : 3319808796 ISBN 13 : 9783319808796

Editeur : Birkh�user, 2018

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This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors.
The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach.
The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics.

Les informations fournies dans la section � Synopsis � peuvent faire r�f�rence � une autre �dition de ce titre.

� propos de l?auteur

Peter Loeb is an emeritus Professor of Mathematics at the University of Illinois in Champaign-Urbana. His research is centered on problems of real analysis and applications of model theory to real analysis.

Les informations fournies dans la section � A propos du livre � peuvent faire r�f�rence � une autre �dition de ce titre.

�diteur: Birkh�user
Date d'�dition: 2018
Langue: anglais
ISBN 10: 3319808796
ISBN 13: 9783319808796
Reliure: Broch�
Nombre de pages: 288
Coordonn�es du fabricant: ProductSafety@springernature.com
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Allemagne

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Real Analysis (eng)

Loeb, Peter A.

Edit� par Birkh�user, 2018

ISBN 10 : 3319808796 ISBN 13 : 9783319808796

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Real Analysis

Peter A. Loeb

Edit� par Birkh�user, Springer Mai 2018, 2018

ISBN 10 : 3319808796 ISBN 13 : 9783319808796

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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors.The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach.The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics. 288 pp. Englisch. N� de r�f. du vendeur 9783319808796

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Real Analysis

Peter A. Loeb

Edit� par Springer International Publishing, 2018

ISBN 10 : 3319808796 ISBN 13 : 9783319808796

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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Written by one of the leading scholars in the field&nbspIncludes a novel presentation of differentiation and absolute continuity using a local maximum function,&nbspresulting in an exposition that is both simpler and more general than the traditional. N� de r�f. du vendeur 458621249

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Real Analysis

Peter A. Loeb

Edit� par Birkh�user, Springer Mai 2018, 2018

ISBN 10 : 3319808796 ISBN 13 : 9783319808796

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Taschenbuch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors.Springer-Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 288 pp. Englisch. N� de r�f. du vendeur 9783319808796

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Real Analysis

Peter A. Loeb

Edit� par Birkh�user, Springer, 2018

ISBN 10 : 3319808796 ISBN 13 : 9783319808796

Neuf Taschenbuch

Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne

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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This textbook is designed for a year-long course in real analysis taken by beginning graduate and advanced undergraduate students in mathematics and other areas such as statistics, engineering, and economics. Written by one of the leading scholars in the field, it elegantly explores the core concepts in real analysis and introduces new, accessible methods for both students and instructors.The first half of the book develops both Lebesgue measure and, with essentially no additional work for the student, general Borel measures for the real line. Notation indicates when a result holds only for Lebesgue measure. Differentiation and absolute continuity are presented using a local maximal function, resulting in an exposition that is both simpler and more general than the traditional approach.The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. To correctly discuss weak limits of measures, one needs the notion of a topological space rather than just a metric space, so general topology is introduced in terms of a base of neighborhoods at a point. The development of results then proceeds in parallel with results for metric spaces, where the base is generated by balls centered at a point. The text concludes with appendices on covering theorems for higher dimensions and a short introduction to nonstandard analysis including important applications to probability theory and mathematical economics. N� de r�f. du vendeur 9783319808796

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