Measure and Integration: A Concise Introduction to Real Analysis

A uniquely accessible book for general measure and integration,emphasizing the real line, Euclidean space, and the underlying roleof translation in real analysis

Measure and Integration: A Concise Introduction to RealAnalysis presents the basic concepts and methods that areimportant for successfully reading and understanding proofs.Blending coverage of both fundamental and specialized topics, thisbook serves as a practical and thorough introduction to measure andintegration, while also facilitating a basic understanding of realanalysis.

The author develops the theory of measure and integration onabstract measure spaces with an emphasis of the real line andEuclidean 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′stheorem
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 dualitytheorems
Translation–invariant subspaces of L2 and applications

The book′s presentation lays the foundation for further study offunctional analysis, harmonic analysis, and probability, and itstreatment of real analysis highlights the fundamental role oftranslations. Each theorem is accompanied by opportunities toemploy the concept, as numerous exercises explore applicationsincluding convolutions, Fourier transforms, and differentiationacross the integral sign.

Providing an efficient and readable treatment of this classicalsubject, Measure and Integration: A Concise Introduction to RealAnalysis is a useful book for courses in real analysis at thegraduate level. It is also a valuable reference for practitionersin the mathematical sciences.