The theory of measures and integration

Eric M. Vestrup - Collection Wiley Series in Probability and Statistics

608 pages, parution le 17/10/2003

Ajouter à une liste

Indisponible

Résumé

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.

Set Systems
Measures
Extensions of Measures
Lebesgue Measure
Measurable Functions
The Lebesgue Integral
Integrals Relative to Lebesgue Measure
The Lp Space
The Radon-Nikodym Theorem
Products of Two Measure Spaces
Arbitrary Products of Measure Spaces
References
Index

L'auteur - Eric M. Vestrup

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.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Eric M. Vestrup
Collection	Wiley Series in Probability and Statistics
Parution	17/10/2003
Nb. de pages	608
Format	16 x 24
Couverture	Relié
Poids	975g
Intérieur	Noir et Blanc
EAN13	9780471249771
ISBN13	978-0-471-24977-1