A Course on Integration Theory | Taschenbuch

Cover: 9783034806930 | A Course on Integration Theory | Nicolas Lerner | Taschenbuch | xviii

Rückseite: 9783034806930 | A Course on Integration Theory | Nicolas Lerner | Taschenbuch | xviii

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Sprache: Englisch

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Beschreibung

This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathéodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change of variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality are proven. The Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems, including Marcinkiewicz's theorem, the definition of Lebesgue points and Lebesgue differentiation theorem are further topics included. A detailed appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. The appendix also provides more advanced material such as some basic properties of cardinals and ordinals which are useful in the study of measurability.¿

Über den Autor

Nicolas Lerner is Professor at Université Pierre and Marie Curie in Paris, France. He held professorial positions in the United States (Purdue University), and in France. His research work is concerned with microlocal analysis and partial differential equations. His recent book Metrics on the Phase Space and Non-Selfadjoint Pseudodifferential Operators was published by Birkhäuser. He was an invited section speaker at the Beijing International Congress of Mathematicians in 2002.

Zusammenfassung

Includes over 150 exercises with detailed solutions

Requires no prior knowledge of advanced mathematics although the results proven in the book are not elementary

Is self-contained, providing detailed arguments for each statement

Includes a helpful appendix to recall basic notions

Inhaltsverzeichnis

1 Introduction.- 2 General theory of integration.- 3 Construction of the Lebesgue measure on R^d.- 4 Spaces of integrable functions.- 5 Integration on a product space.- 6 Diffeomorphisms of open subsets of R^d and integration.- 7 Convolution.- 8 Complex measures.- 9 Harmonic analysis.- 10 Classical inequalities.

Details

Erscheinungsjahr:	2014
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xviii 492 S. 12 s/w Illustr. 3 farbige Illustr. 492 p. 15 illus. 3 illus. in color.
ISBN-13:	9783034806930
ISBN-10:	3034806930
Sprache:	Englisch
Herstellernummer:	86288668
Einband:	Kartoniert / Broschiert
Autor:	Lerner, Nicolas
Hersteller:	Springer Birkhäuser Springer Basel AG
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	235 x 155 x 28 mm
Von/Mit:	Nicolas Lerner
Erscheinungsdatum:	17.03.2014
Gewicht:	0,768 kg