Wiley
Wiley.com
Print this page Share

The Theory of Measures and Integration

ISBN: 978-0-471-24977-1
624 pages
September 2003
The Theory of Measures and Integration (0471249777) cover image
An accessible, clearly organized survey of the basic topics of measure theory for students and researchers in mathematics, statistics, and physics
In order to fully understand and appreciate advanced probability, analysis, and advanced mathematical statistics, a rudimentary knowledge of measure theory and like subjects must first be obtained. The Theory of Measures and Integration illuminates the fundamental ideas of the subject-fascinating in their own right-for both students and researchers, providing a useful theoretical background as well as a solid foundation for further inquiry.
Eric Vestrup's patient and measured text presents the major results of classical measure and integration theory in a clear and rigorous fashion. Besides offering the mainstream fare, the author also offers detailed discussions of extensions, the structure of Borel and Lebesgue sets, set-theoretic considerations, the Riesz representation theorem, and the Hardy-Littlewood theorem, among other topics, employing a clear presentation style that is both evenly paced and user-friendly. Chapters include:
* Measurable Functions
* The Lp Spaces
* The Radon-Nikodym Theorem
* Products of Two Measure Spaces
* Arbitrary Products of Measure Spaces
Sections conclude with exercises that range in difficulty between easy "finger exercises"and substantial and independent points of interest. These more difficult exercises are accompanied by detailed hints and outlines. They demonstrate optional side paths in the subject as well as alternative ways of presenting the mainstream topics.
In writing his proofs and notation, Vestrup targets the person who wants all of the details shown up front. Ideal for graduate students in mathematics, statistics, and physics, as well as strong undergraduates in these disciplines and practicing researchers, The Theory of Measures and Integration proves both an able primary text for a real analysis sequence with a focus on measure theory and a helpful background text for advanced courses in probability and statistics.
See More
Preface.

Acknowledgments.

1. Set Systems.

2. Measures.

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.

References.

Index.

See More
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.
See More
"…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)

See More
Buy Both and Save 25%!
+

The Theory of Measures and Integration (US $171.00)

-and- Bayesian Analysis of Stochastic Process Models (US $107.95)

Total List Price: US $278.95
Discounted Price: US $209.21 (Save: US $69.74)

Buy Both
Cannot be combined with any other offers. Learn more.

Related Titles

Back to Top