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Posted on 2010-12-06, updated at 2012-11-16. By anonymous.
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Measure and Integral: An Introduction to Real Analysis
288 pages | Dec 12, 2007 |ISBN:0824764994 | PDF | 8 Mb
This volume develops the classical theory of the Lebesgue integral and some of its applications. Following a thorough study of the concepts of outer measure and measure, the author initially presents the integral in the context of n-dimensional Euclidean space. A more general treatment of the integral, based on an axiomatic approach, is given later. The book examines closely related topics in real variables, such as functions of bounded variation, the Riemann-Stieltjes integral, Fubini's theorem, L(p) classes, and various results about differentiation. Several applications of the theory to a specific branch of analysis-harmonic analysis-are also provided.
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