measuring tape
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 role of translation in real analysis p 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 . p 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 p measure spaces outer measures and extension theorems p lebesgue measure on the line and in euclidean space p measurable functions egoroffs theorem and lusins theorem p convergence theorems for integrals p product measures and fubinis theorem p differentiation theorems for functions of real variables p decomposition theorems for signed measures p absolute continuity and the radon nikodym theorem p lp spaces continuous function spaces and duality theorems p translation invariant subspaces of l2 and applications p the books 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 . p 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 .