The Theory of Measures and Integration / Edition 1 available in Hardcover
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An accessible, clearly organized survey of the basic topics ofmeasure theory for students and researchers in mathematics,statistics, and physicsIn order to fully understand and appreciate advanced probability,analysis, and advanced mathematical statistics, a rudimentaryknowledge of measure theory and like subjects must first beobtained. The Theory of Measures and Integration illuminates thefundamental ideas of the subject-fascinating in their own right-forboth students and researchers, providing a useful theoreticalbackground as well as a solid foundation for further inquiry.Eric Vestrup's patient and measured text presents the major resultsof classical measure and integration theory in a clear and rigorousfashion. Besides offering the mainstream fare, the author alsooffers detailed discussions of extensions, the structure of Boreland Lebesgue sets, set-theoretic considerations, the Rieszrepresentation theorem, and the Hardy-Littlewood theorem, amongother topics, employing a clear presentation style that is bothevenly paced and user-friendly. Chapters include:* Measurable Functions* The Lp Spaces* The Radon-Nikodym Theorem* Products of Two Measure Spaces* Arbitrary Products of Measure SpacesSections conclude with exercises that range in difficulty betweeneasy "finger exercises"and substantial and independent points ofinterest. These more difficult exercises are accompanied bydetailed hints and outlines. They demonstrate optional side pathsin the subject as well as alternative ways of presenting themainstream topics.In writing his proofs and notation, Vestrup targets the person whowants all of the details shown up front. Ideal for graduatestudents in mathematics, statistics, and physics, as well as strongundergraduates in these disciplines and practicing researchers, TheTheory of Measures and Integration proves both an able primary textfor a real analysis sequence with a focus on measure theory and ahelpful background text for advanced courses in probability andstatistics.
About the Author
ERIC M. VESTRUP received his master’s and doctorate in statistics from the University of California at Davis. He was awarded the Chancellor’s Teaching Fellowship prize from UC Davis in 1997 for outstanding promise in the field of teaching. He has published in the areas of mathematical statistics, decision theory, and analytic philosophy, and is currently an assistant professor at DePaul University.
Table of Contents
1. Set Systems.
3. Extensions of Measures.
4. Lebesgue Measure.
5. Measurable Functions.
6. The Lebesgue Integral.
7. Integrals Relative to Lebesgue Measure.
8. The Lp Spaces.
9. The Radon–Nikodym Theorem.
10. Products of Two Measure Spaces.
11. Arbitrary Products of Measure Spaces.
What People are Saying About This
"…an excellent read…I was impressed with the wealth of information and the amount of flawless detail." (Journal of the American Statistical Association, March 2006)
“…contains many really good exercises…the style is clear and the notation appropriate…” (Zentralbaltt MATH, May 2005)