A Course on Integration Theory: including more than 150 exercises with detailed answers - Tapa blanda

Lerner, Nicolas

 
9783034806930: A Course on Integration Theory: including more than 150 exercises with detailed answers
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ISBN 10: 3034806930 ISBN 13: 9783034806930
Editorial: Birkhäuser, 2014

Sinopsis

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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Acerca del 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.

De la contraportada

<p>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. Further topics include the Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems including Marcinkiewicz's theorem, and the definition of Lebesgue points and the Lebesgue differentiation theorem. </p><p>Each chapter ends with a large number of exercises and detailed solutions. </p><p>A comprehensive appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. It also provides more advanced material such as some basic properties of cardinals and ordinals which are useful for the study of measurability.</p>

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Editorial
Birkhäuser
Año de publicación
2014
Idioma
Inglés
ISBN 10 
3034806930
ISBN 13 
9783034806930
Encuadernación
Tapa blanda
Número de páginas
512
Contacto del fabricante
no disponible
Persona responsable
CMN Printpool Inh. Mathis Neumann
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Hamburg
Alemania

Otras ediciones populares con el mismo título

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

Edición Destacada

ISBN 10:  3034806957 ISBN 13:  9783034806954
Editorial: Birkhäuser, 2014
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