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Field name	Details
Dewey Class	515.8
Title	A Course on Integration Theory ([Ebook]) : including more than 150 exercises with detailed answers / by Nicolas Lerner.
Author	Lerner, Nicolas
Other name(s)	SpringerLink (Online service)
Publication	Basel Birkhäuser 2014.
Physical Details	XVIII, 492 p. 15 illus., 3 illus. in color. : online resource.
ISBN	9783034806947
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-0694-7
Links to Related Works	Subject References: Mathematics . Measure and Integration . Real Functions . Authors: Lerner, Nicolas . Corporate Authors: SpringerLink (Online service) . Classification: 515.8 .

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

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