Measure and Integration A Concise Introduction to Real Analysis
105,99 €
inkl. gesetzl. MwSt.Beschreibung
Produktdetails
Format
Kopierschutz
Ja
Family Sharing
Nein
Text-to-Speech
Nein
Erscheinungsdatum
01.07.2009
Verlag
WileySeitenzahl
256 (Printausgabe)
Dateigröße
8565 KB
Auflage
1. Auflage
Sprache
Englisch
EAN
9780470501146
A uniquely accessible book for general measure and integration,
emphasizing the real line, Euclidean space, and the underlying role
of translation in real analysis
Measure and Integration: A Concise Introduction to Real
Analysis presents the basic concepts and methods that are
important for successfully reading and understanding proofs.
Blending coverage of both fundamental and specialized topics, this
book serves as a practical and thorough introduction to measure and
integration, while also facilitating a basic understanding of real
analysis.
The author develops the theory of measure and integration on
abstract measure spaces with an emphasis of the real line and
Euclidean space. Additional topical coverage includes:
* Measure spaces, outer measures, and extension theorems
* Lebesgue measure on the line and in Euclidean space
* Measurable functions, Egoroff's theorem, and Lusin's
theorem
* Convergence theorems for integrals
* Product measures and Fubini's theorem
* Differentiation theorems for functions of real variables
* Decomposition theorems for signed measures
* Absolute continuity and the Radon-Nikodym theorem
* Lp spaces, continuous-function spaces, and duality
theorems
* Translation-invariant subspaces of L2 and applications
The book's presentation lays the foundation for further study of
functional analysis, harmonic analysis, and probability, and its
treatment of real analysis highlights the fundamental role of
translations. Each theorem is accompanied by opportunities to
employ the concept, as numerous exercises explore applications
including convolutions, Fourier transforms, and differentiation
across the integral sign.
Providing an efficient and readable treatment of this classical
subject, Measure and Integration: A Concise Introduction to Real
Analysis is a useful book for courses in real analysis at the
graduate level. It is also a valuable reference for practitioners
in the mathematical sciences.
emphasizing the real line, Euclidean space, and the underlying role
of translation in real analysis
Measure and Integration: A Concise Introduction to Real
Analysis presents the basic concepts and methods that are
important for successfully reading and understanding proofs.
Blending coverage of both fundamental and specialized topics, this
book serves as a practical and thorough introduction to measure and
integration, while also facilitating a basic understanding of real
analysis.
The author develops the theory of measure and integration on
abstract measure spaces with an emphasis of the real line and
Euclidean space. Additional topical coverage includes:
* Measure spaces, outer measures, and extension theorems
* Lebesgue measure on the line and in Euclidean space
* Measurable functions, Egoroff's theorem, and Lusin's
theorem
* Convergence theorems for integrals
* Product measures and Fubini's theorem
* Differentiation theorems for functions of real variables
* Decomposition theorems for signed measures
* Absolute continuity and the Radon-Nikodym theorem
* Lp spaces, continuous-function spaces, and duality
theorems
* Translation-invariant subspaces of L2 and applications
The book's presentation lays the foundation for further study of
functional analysis, harmonic analysis, and probability, and its
treatment of real analysis highlights the fundamental role of
translations. Each theorem is accompanied by opportunities to
employ the concept, as numerous exercises explore applications
including convolutions, Fourier transforms, and differentiation
across the integral sign.
Providing an efficient and readable treatment of this classical
subject, Measure and Integration: A Concise Introduction to Real
Analysis is a useful book for courses in real analysis at the
graduate level. It is also a valuable reference for practitioners
in the mathematical sciences.
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