A Course on Integration Theory: Including More Than 150 Exercises With Detailed Answers - Couverture souple

Lerner, Nicolas

 
9783034806930: A Course on Integration Theory: Including More Than 150 Exercises With Detailed Answers
Couverture souple
ISBN 10 : 3034806930 ISBN 13 : 9783034806930
Editeur : Springer Basel, 2014

Synopsis

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.​

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À propos de l?auteur

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.

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Éditeur
Springer Basel
Date d'édition
2014
Langue
anglais
ISBN 10 
3034806930
ISBN 13 
9783034806930
Reliure
Broché
Nombre de pages
492
Coordonnées du fabricant
non disponible
Personne responsable
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Autres éditions populaires du même titre

9783034806954: A Course on Integration Theory: including more than 150 exercises with detailed answers

Edition présentée

ISBN 10 :  3034806957 ISBN 13 :  9783034806954
Editeur : Birkhäuser, 2014
Couverture souple