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Real Analysis
Buch von Emmanuele Dibenedetto
Sprache: Englisch

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Beschreibung
The second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid foundation for future coursework and research in applied mathematics. Written in a clear and concise style, it covers all of the necessary subjects as well as those often absent from standard introductory texts. Each chapter features a ¿Problems and Complements¿ section that includes additional material that briefly expands on certain topics within the chapter and numerous exercises for practicing the key concepts.
The first eight chapters explore all of the basic topics for training in real analysis, beginning with a review of countable sets before moving on to detailed discussions of measure theory, Lebesgue integration, Banach spaces, functional analysis, and weakly differentiable functions. More topical applications are discussed in the remaining chapters, such as maximal functions, functions of bounded mean oscillation, rearrangements, potential theory, and the theory of Sobolev functions. This second edition has been completely revised and updated and contains a variety of new content and expanded coverage of key topics, such as new exercises on the calculus of distributions, a proof of the Riesz convolution, Steiner symmetrization, and embedding theorems for functions in Sobolev spaces.
Ideal for either classroom use or self-study, Real Analysis is an excellent textbook both for students discovering real analysis for the first time and for mathematicians and researchers looking for a useful resource for reference or review.
Praise for the First Edition:
¿[This book] will be extremely useful as a text. There is certainly enough material for a year-long graduate course, but judicious selection would make it possible to use this most appealing book in a one-semester course for well-prepared students.¿
¿Mathematical Reviews
The second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid foundation for future coursework and research in applied mathematics. Written in a clear and concise style, it covers all of the necessary subjects as well as those often absent from standard introductory texts. Each chapter features a ¿Problems and Complements¿ section that includes additional material that briefly expands on certain topics within the chapter and numerous exercises for practicing the key concepts.
The first eight chapters explore all of the basic topics for training in real analysis, beginning with a review of countable sets before moving on to detailed discussions of measure theory, Lebesgue integration, Banach spaces, functional analysis, and weakly differentiable functions. More topical applications are discussed in the remaining chapters, such as maximal functions, functions of bounded mean oscillation, rearrangements, potential theory, and the theory of Sobolev functions. This second edition has been completely revised and updated and contains a variety of new content and expanded coverage of key topics, such as new exercises on the calculus of distributions, a proof of the Riesz convolution, Steiner symmetrization, and embedding theorems for functions in Sobolev spaces.
Ideal for either classroom use or self-study, Real Analysis is an excellent textbook both for students discovering real analysis for the first time and for mathematicians and researchers looking for a useful resource for reference or review.
Praise for the First Edition:
¿[This book] will be extremely useful as a text. There is certainly enough material for a year-long graduate course, but judicious selection would make it possible to use this most appealing book in a one-semester course for well-prepared students.¿
¿Mathematical Reviews
Über den Autor
Emmanuele DiBenedetto is Centennial Professor of Mathematics at Vanderbilt University, Nashville, TN, USA.
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
Preliminaries.- Topologies and Metric Spaces.- Measuring Sets.- The Lebesgue Integral.- Topics on Measurable Functions of Real Variables.- The L^p Spaces.- Banach Spaces.- Spaces of Continuous Functions, Distributions, and Weak Derivatives.- Topics on Integrable Functions of Real Variables.- Embedding of W ^1,p (E) into L^q (E).- Topics on Weakly Differentiable Functions.- References.- Index.
Details
Erscheinungsjahr: 2016
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 628
Reihe: Birkhäuser Advanced Texts Basler Lehrbücher
Inhalt: xxxii
596 S.
4 s/w Illustr.
596 p. 4 illus.
ISBN-13: 9781493940035
ISBN-10: 1493940031
Sprache: Englisch
Herstellernummer: 978-1-4939-4003-5
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Dibenedetto, Emmanuele
Auflage: 2nd ed. 2016
Hersteller: Springer US
Springer New York
Birkhäuser Advanced Texts Basler Lehrbücher
Maße: 241 x 160 x 38 mm
Von/Mit: Emmanuele Dibenedetto
Erscheinungsdatum: 18.09.2016
Gewicht: 1,097 kg
preigu-id: 103864278
Über den Autor
Emmanuele DiBenedetto is Centennial Professor of Mathematics at Vanderbilt University, Nashville, TN, USA.
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
Preliminaries.- Topologies and Metric Spaces.- Measuring Sets.- The Lebesgue Integral.- Topics on Measurable Functions of Real Variables.- The L^p Spaces.- Banach Spaces.- Spaces of Continuous Functions, Distributions, and Weak Derivatives.- Topics on Integrable Functions of Real Variables.- Embedding of W ^1,p (E) into L^q (E).- Topics on Weakly Differentiable Functions.- References.- Index.
Details
Erscheinungsjahr: 2016
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 628
Reihe: Birkhäuser Advanced Texts Basler Lehrbücher
Inhalt: xxxii
596 S.
4 s/w Illustr.
596 p. 4 illus.
ISBN-13: 9781493940035
ISBN-10: 1493940031
Sprache: Englisch
Herstellernummer: 978-1-4939-4003-5
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Dibenedetto, Emmanuele
Auflage: 2nd ed. 2016
Hersteller: Springer US
Springer New York
Birkhäuser Advanced Texts Basler Lehrbücher
Maße: 241 x 160 x 38 mm
Von/Mit: Emmanuele Dibenedetto
Erscheinungsdatum: 18.09.2016
Gewicht: 1,097 kg
preigu-id: 103864278
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