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Real and Functional Analysis

  • Textbook
  • © 1993

Overview

Authors:
  1. Serge Lang

    1. Department of Mathematics, Yale University, New Haven, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 142)

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-xiv
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  2. General Topology

    1. Front Matter

      Pages 1-1
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    2. Sets

      • Serge Lang
      Pages 3-16

    3. Topological Spaces

      • Serge Lang
      Pages 17-50

    4. Continuous Functions on Compact Sets

      • Serge Lang
      Pages 51-62

  3. Banach and Hilbert Spaces

    1. Front Matter

      Pages 63-63
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    2. Banach Spaces

      • Serge Lang
      Pages 65-94

    3. Hilbert Space

      • Serge Lang
      Pages 95-108

  4. Integration

    1. Front Matter

      Pages 109-110
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    2. The General Integral

      • Serge Lang
      Pages 111-180

    3. Duality and Representation Theorems

      • Serge Lang
      Pages 181-222

    4. Some Applications of Integration

      • Serge Lang
      Pages 223-250

    5. Integration and Measures on Locally Compact Spaces

      • Serge Lang
      Pages 251-277

    6. Riemann-Stieltjes Integral and Measure

      • Serge Lang
      Pages 278-294

    7. Distributions

      • Serge Lang
      Pages 295-307

    8. Integration on Locally Compact Groups

      • Serge Lang
      Pages 308-328

  5. Calculus

    1. Front Matter

      Pages 329-329
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    2. Differential Calculus

      • Serge Lang
      Pages 331-359

    3. Inverse Mappings and Differential Equations

      • Serge Lang
      Pages 360-384

  6. Functional Analysis

    1. Front Matter

      Pages 385-386
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Keywords

About this book

This book is meant as a text for a first year graduate course in analysis. Any standard course in undergraduate analysis will constitute sufficient preparation for its understanding, for instance, my Undergraduate Anal­ ysis. I assume that the reader is acquainted with notions of uniform con­ vergence and the like. In this third edition, I have reorganized the book by covering inte­ gration before functional analysis. Such a rearrangement fits the way courses are taught in all the places I know of. I have added a number of examples and exercises, as well as some material about integration on the real line (e.g. on Dirac sequence approximation and on Fourier analysis), and some material on functional analysis (e.g. the theory of the Gelfand transform in Chapter XVI). These upgrade previous exercises to sections in the text. In a sense, the subject matter covers the same topics as elementary calculus, viz. linear algebra, differentiation and integration. This time, however, these subjects are treated in a manner suitable for the training of professionals, i.e. people who will use the tools in further investiga­ tions, be it in mathematics, or physics, or what have you. In the first part, we begin with point set topology, essential for all analysis, and we cover the most important results.

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Serge Lang

Bibliographic Information

  • Book Title: Real and Functional Analysis

  • Authors: Serge Lang

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0897-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1993

  • Hardcover ISBN: 978-0-387-94001-4Published: 29 April 1993

  • Softcover ISBN: 978-1-4612-6938-0Published: 23 October 2012

  • eBook ISBN: 978-1-4612-0897-6Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 3

  • Number of Pages: XIV, 580

  • Additional Information: Originally published by Addison Wesley, 1983

  • Topics: Analysis, Real Functions

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