Measure and integration
WORLDSHARE SUB RECORDS
Salamon, D. (Dietmar)
creator
author.
text
bibliography
sz
Zürich, Switzerland
European Mathematical Society Publishing House
2016
monographic
eng
access
1 online resource (363 pages)
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.
Abstract measure theory -- The Lebesgue measure -- Borel measures -- L [superscript p] spaces -- The Radon-Nikodým theorem -- Differentiation -- Product measures -- The Haar measure -- Appendices.
specialized
Dietmar A. Salamon.
Includes bibliographical references (pages 347-394), and index.
Measure theory
QA312
515.43
28-xx
(DLC) 2016427659
(OCoLC)946976314
EMS textbooks in mathematics
9783037196595
3037196599
3037191597
9783037191590
3037196599
3037191597
9783037191590
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LLB
160229
20210517053725.2
mig00005363913
eng