Measure and integration /

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, $L̂p$ spaces and their dua...

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Bibliographic Details
Main Author: Salamon, D. (Author)
Format: eBook
Language:English
Published: Zürich, Switzerland : European Mathematical Society Publishing House, 2016.
Series:EMS textbooks in mathematics.
Subjects:
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245 1 0 |a Measure and integration /  |c Dietmar A. Salamon. 
260 3 |a Zürich, Switzerland :  |b European Mathematical Society Publishing House,  |c 2016. 
300 |a 1 online resource (363 pages) 
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504 |a Includes bibliographical references (pages 347-394), and index. 
505 0 |a Abstract measure theory -- The Lebesgue measure -- Borel measures -- L [superscript p] spaces -- The Radon-Nikodým theorem -- Differentiation -- Product measures -- The Haar measure -- Appendices. 
520 |a 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, $L̂p$ 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 desiring an introduction to the concepts of measure and integration. 
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