Foundations of real and abstract analysis

Douglas S. Bridges

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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[目次]

  • 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.

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この本の情報

書名 Foundations of real and abstract analysis
著作者等 Bridges, D. S.
Bridges Douglas
シリーズ名 Graduate texts in mathematics
出版元 Springer
刊行年月 c1998
ページ数 xiv, 322 p.
大きさ 25 cm
ISBN 0387982396
NCID BA33547516
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言語 英語
出版国 アメリカ合衆国
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