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Measure and Integration

โœ Scribed by Dietmar A. Salamon

Publisher
European Mathematical Society
Year
2016
Tongue
English
Leaves
365
Series
EMS Textbooks in Mathematics
Category
Library
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โœฆ Synopsis

The book is intended as a companion to a one-semester introductory lecture course on measure and integration. After an introduction to abstract measure theory, it proceeds to the construction of the Lebesgue measure and of Borel measures on locally compact Hausdorff spaces, Lp spaces and their dual spaces, and elementary Hilbert space theory. Special features include the formulation of the Riesz representation theorem in terms of both inner and outer regularity, the proofs of the Marcinkiewicz interpolation theorem, and the Calderon Zygmund inequality as applications of Fubini's theorem and Lebesgue differentiation, the treatment of the generalized Radon Nikodym theorem due to Fremlin, and the existence proof for Haar measures. Three appendices deal with Urysohn's Lemma, product topologies, and the inverse function theorem. The book assumes familiarity with first-year analysis and linear algebra. It is suitable for second-year undergraduate students of mathematics or anyone seeking an introduction to the concepts of measure and integration

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<p>This book covers the material of a one year course in real analysis.ย  It includes an original axiomatic approach to Lebesgue integration which the authors have found to be effective in the classroom.ย  Each chapter contains numerous examples and an extensive problem set which expands considerably

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