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Sinossi
Concise in treatment and comprehensive in scope, this text for graduate students in mathematics introduces contemporary real analysis with a particular emphasis on integration theory.
The first four chapters, dealing with the Lebesgue theory of measure and integration of real functions, constitute a critical study of differential and integral calculus. Succeeding chapters treat abstract measure and integration theory, as well as topological and metric spaces, with an emphasis on topics that are most relevant to analysis. Additional subjects include a discussion of Stone's formulation of Daniell integration, culminating in the Riesz representation theorem, and an examination of normed linear spaces. Exercise sections appear at the end of each chapter and form an integral part of the text.
The first four chapters, dealing with the Lebesgue theory of measure and integration of real functions, constitute a critical study of differential and integral calculus. Succeeding chapters treat abstract measure and integration theory, as well as topological and metric spaces, with an emphasis on topics that are most relevant to analysis. Additional subjects include a discussion of Stone's formulation of Daniell integration, culminating in the Riesz representation theorem, and an examination of normed linear spaces. Exercise sections appear at the end of each chapter and form an integral part of the text.
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Contenuti
1. Lebesgue Measure on the Real Line R1 2. Lebesgue Measurable Functions on the Real Line 3. The Lebesgue Integral on the Real Line R1 and the Lebesgue Function Spaces 4. Differentiation and Absolute Continuity 5. Abstract Measure and Integration 6. Outer Measure and Product Measure 7. Topological and Metric Spaces 8. The Method of P. J. Daniell 9. The Stone-Daniell Integral (A Survey) 10. Normed Linear Spaces Index
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Real Analysis, Gabriel Klambauer, 9780486445243, Dover Publications, 2005, Paperback
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