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Infinite Dimensional Analysis

A Hitchhiker's Guide

  • Book
  • © 2006

Overview

Authors:
  1. Charalambos D. Aliprantis

    1. Department of Economics, Krannert School of Management, West Lafayette, USA
      Purdue University, West Lafayette, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Kim C. Border

    1. Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, USA

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    You can also search for this author in PubMed   Google Scholar

  • First book to present functional analysis in a unified manner with applications to economics, social sciences, and engineering
  • With lots of new and important material and additional applications
  • Includes supplementary material: sn.pub/extras

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xxii
    Download chapter PDF

  2. Odds and ends

    Pages 1-20

  3. Topology

    Pages 21-67

  4. Metrizable spaces

    Pages 69-126

  5. Measurability

    Pages 127-161

  6. Topological vector spaces

    Pages 163-224

  7. Normed spaces

    Pages 225-250

  8. Convexity

    Pages 251-309

  9. Riesz spaces

    Pages 311-345

  10. Banach lattices

    Pages 347-370

  11. Charges and measures

    Pages 371-402

  12. Integrals

    Pages 403-432

  13. Measures and topology

    Pages 433-460

  14. Lp-spaces

    Pages 461-486

  15. Riesz Representation Theorems

    Pages 487-503

  16. Probability measures

    Pages 505-523

  17. Spaces of sequences

    Pages 525-554

  18. Correspondences

    Pages 555-590

  19. Measurable correspondences

    Pages 591-620

  20. Markov transitions

    Pages 621-653
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Keywords

About this book

This new edition of The Hitchhiker’s Guide has bene?tted from the comments of many individuals, which have resulted in the addition of some new material, and the reorganization of some of the rest. The most obvious change is the creation of a separate Chapter 7 on convex analysis. Parts of this chapter appeared in elsewhere in the second edition, but much of it is new to the third edition. In particular, there is an expanded discussion of support points of convex sets, and a new section on subgradients of convex functions. There is much more material on the special properties of convex sets and functions in ?nite dimensional spaces. There are improvements and additions in almost every chapter. There is more new material than might seem at ?rst glance, thanks to a change in font that - duced the page count about ?ve percent. We owe a huge debt to Valentina Galvani, Daniela Puzzello, and Francesco Rusticci, who were participants in a graduate seminar at Purdue University and whose suggestions led to many improvements, especially in chapters ?ve through eight. We particularly thank Daniela Puzzello for catching uncountably many errors throughout the second edition, and simplifying the statements of several theorems and proofs. In another graduate seminar at Caltech, many improvements and corrections were suggested by Joel Grus, PJ Healy, Kevin Roust, Maggie Penn, and Bryan Rogers.

Authors and Affiliations

  • Department of Economics, Krannert School of Management, West Lafayette, USA

    Charalambos D. Aliprantis

  • Purdue University, West Lafayette, USA

    Charalambos D. Aliprantis

  • Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, USA

    Kim C. Border

Bibliographic Information

  • Book Title: Infinite Dimensional Analysis

  • Book Subtitle: A Hitchhiker's Guide

  • Authors: Charalambos D. Aliprantis, Kim C. Border

  • DOI: https://doi.org/10.1007/3-540-29587-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Business and Economics, Economics and Finance (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2006

  • Hardcover ISBN: 978-3-540-29586-0Published: 19 May 2006

  • Softcover ISBN: 978-3-540-32696-0Published: 02 May 2007

  • eBook ISBN: 978-3-540-29587-7Published: 08 August 2006

  • Edition Number: 3

  • Number of Pages: XXII, 704

  • Topics: Economic Theory/Quantitative Economics/Mathematical Methods, Functional Analysis

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