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

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 integra...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Lerner, Nicolas (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Springer Basel : Imprint: Birkhäuser, 2014.
Edición:1st ed. 2014.
Temas:
Functions of real variables.
Measure theory.
Real Functions.
Measure and Integration.
Acceso en línea:Texto Completo

MARC

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100 1 |a Lerner, Nicolas.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 2 |a A Course on Integration Theory  |h [electronic resource] :  |b including more than 150 exercises with detailed answers /  |c by Nicolas Lerner. 
250 |a 1st ed. 2014. 
264 1 |a Basel :  |b Springer Basel :  |b Imprint: Birkhäuser,  |c 2014. 
300 |a XVIII, 492 p. 15 illus., 3 illus. in color.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
505 0 |a 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. 
520 |a 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. Each chapter ends with a large number of exercises and detailed solutions. 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. 
650 0 |a Functions of real variables. 
650 0 |a Measure theory. 
650 1 4 |a Real Functions. 
650 2 4 |a Measure and Integration. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783034806954 
776 0 8 |i Printed edition:  |z 9783034806930 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-0348-0694-7  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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