Foundations of Real and Abstract Analysis: 174 - Rilegato

Bridges, Douglas S.

 
9780387982397: Foundations of Real and Abstract Analysis: 174

Sinossi

A complete course on metric, normed, and Hilbert spaces, including many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format, including elementary real analysis, Lebesgue integration on R, and an introduction to functional analysis. The book begins with a fast-paced course on real analysis, followed by an introduction to the Lebesgue integral. This provides a reference for later chapters as well as a preparation for students with only the typical sequence of undergraduate calculus courses as prerequisites. Other features include a chapter introducing functional analysis, the Hahn-Banach theorem and duality, separation theorems, the Baire Category Theorem, the Open Mapping Theorem and their consequences, and unusual applications. Of special interest are the 750 exercises, many with guidelines for their solutions, applications and extensions of the main propositions and theorems, pointers to new branches of the subject, and difficult challenges for the very best students.

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Contenuti

Real Analysis.- Analysis on the Real Line.- Differentiation and the Lebesgue Integral.- Abstract Analysis.- Analysis in Metric Spaces.- Analysis in Normed Linear Spaces.- Hilbert Spaces.- An Introduction to Functional Analysis.

Product Description

Book by Bridges Douglas S

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Altre edizioni note dello stesso titolo

9781475771619: Foundations of Real and Abstract Analysis: 174

Edizione in evidenza

ISBN 10:  1475771614 ISBN 13:  9781475771619
Casa editrice: Springer, 2013
Brossura