Description: Further DetailsTitle: Measure Theory and IntegrationCondition: NewFormat: HardbackEAN: 9780821841808ISBN: 9780821841808Publisher: American Mathematical SocietyGenre: Science Nature & MathRelease Date: 08/30/2006Description: This self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to $L^p$ spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to $L^2$ spaces as Hilbert spaces, with a useful geometrical structure. Having gotten quickly to the heart of the matter, the text proceeds to broaden its scope.There are further constructions of measures, including Lebesgue measure on $n$-dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration of differential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales. This text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory.Language: EnglishCountry/Region of Manufacture: USItem Weight: 745gBook Series: Graduate Studies in MathematicsAuthor: No AuthorRelease Year: 2006 Missing Information?Please contact us if any details are missing and where possible we will add the information to our listing.
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Book Title: Measure Theory and Integration
Title: Measure Theory and Integration
EAN: 9780821841808
ISBN: 9780821841808
Genre: Science Nature & Math
Release Date: 08/30/2006
Release Year: 2006
Country/Region of Manufacture: US
Number of Pages: 319 Pages
Publication Name: Measure Theory and Integration
Language: English
Publisher: American Mathematical Society
Publication Year: 2006
Item Height: 0.9 in
Subject: Functional Analysis, Probability & Statistics / General, Algebra / General
Type: Textbook
Item Weight: 26.5 Oz
Item Length: 10.2 in
Author: American Mathem American Mathem
Subject Area: Mathematics
Series: Graduate Studies in Mathematics Ser.
Item Width: 7.2 in
Format: Hardcover
