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Infinite Dimensional Analysis

A Hitchhiker’s Guide

  • Book
  • © 1999

Overview

Authors:
  1. Charalambos D. Aliprantis

    1. Department of Economics, 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 228-77, California Institute of Technology, Pasadena, USA

    View author publications

    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
  • A modern, clear and comprehensive treatment of functional analysis

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Odds and ends

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 1-18

  3. Topology

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 19-68

  4. Metrizable spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 69-122

  5. Measurability

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 123-160

  6. Topological vector spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 161-236

  7. Normed spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 237-262

  8. Riesz spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 263-300

  9. Banach lattices

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 301-330

  10. Charges and measures

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 331-364

  11. Measures and topology

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 365-394

  12. Integrals

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 395-426

  13. L p -spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 427-454

  14. Riesz Representation Theorems

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 455-472

  15. Probability measures on metrizable spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 473-492

  16. Spaces of sequences

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 493-522

  17. Correspondences

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 523-556

  18. Measurable correspondences

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 557-586

  19. Markov transitions

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 587-620

  20. Ergodicity

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 621-633
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About this book

In the nearly five years since the publication of what we refer to as The Hitchhiker's Guide, we have been the recipients of much advice and many complaints. That, combined with the economics of the publishing industry, convinced us that the world would be a better place if we published a second edition of our book, and made it available in paperback at a more modest price. The most obvious difference between the second and the original edition is the reorganization of material that resulted in three new chapters. Chap­ ter 4 collects many of the purely set-theoretical results about measurable structures such as semirings and a-algebras. The material in this chapter is quite independent from notions of measure and integration, and is easily ac­ cessible, so we thought it should come sooner. We also divided the chapter on correspondences into two separate chapters, one dealing with continuity, the other with measurability. The material on measurable correspondences is more detailed and, we hope, better written. We also put many of the representation theorems into their own Chapter 13. This arrangement has the side effect of forcing the renumbering of almost every result in the text, thus rendering the original version obsolete. We feel bad about that, but like Humpty Dumpty, we doubt we could put it back the way it was. The second most noticeable change is the addition of approximately seventy pages of new material.

Authors and Affiliations

  • Department of Economics, Purdue University, West Lafayette, USA

    Charalambos D. Aliprantis

  • Division of the Humanities and Social Sciences 228-77, California Institute of Technology, Pasadena, USA

    Kim C. Border

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