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Infinite Dimensional Analysis

A Hitchhiker’s Guide

  • Book
  • © 1994

Overview

Authors:
  1. Charalambos D. Aliprantis

    1. Department of Mathematics, Indiana University-Purdue University Indianapolis (IUPUI), Indianapolis, USA

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  2. Kim C. Border

    1. Division of the Humanities and Social Sciences, CALTECH, Pasadena, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Studies in Economic Theory (ECON.THEORY, volume 4)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xviii
    Download chapter PDF

  2. Odds and ends

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 1-19

  3. Topology

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 20-69

  4. Metrizable spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 70-115

  5. Topological vector spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 116-180

  6. Normed spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 181-205

  7. Riesz spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 206-243

  8. Banach lattices

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 244-268

  9. Charges and measures

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 269-310

  10. Integrals

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 311-340

  11. L p -spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 341-367

  12. Measures and topology

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 368-410

  13. Probability measures on metrizable spaces

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 411-427

  14. Spaces of sequences

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 428-457

  15. Correspondences

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 458-520

  16. Markov transitions

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 521-553

  17. Ergodicity

    • Charalambos D. Aliprantis, Kim C. Border
    Pages 554-566

  18. Back Matter

    Pages 567-605
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Keywords

About this book

This text was born out of an advanced mathematical economics seminar at Caltech in 1989-90. We realized that the typical graduate student in mathematical economics has to be familiar with a vast amount of material that spans several traditional fields in mathematics. Much of the mate­ rial appears only in esoteric research monographs that are designed for specialists, not for the sort of generalist that our students need be. We hope that in a small way this text will make the material here accessible to a much broader audience. While our motivation is to present and orga­ nize the analytical foundations underlying modern economics and finance, this is a book of mathematics, not of economics. We mention applications to economics but present very few of them. They are there to convince economists that the material has so me relevance and to let mathematicians know that there are areas of application for these results. We feel that this text could be used for a course in analysis that would benefit math­ ematicians, engineers, and scientists. Most of the material we present is available elsewhere, but is scattered throughout a variety of sources and occasionally buried in obscurity. Some of our results are original (or more likely, independent rediscoveries). We have included some material that we cannot honestly say is neces­ sary to understand modern economic theory, but may yet prove useful in future research.

Authors and Affiliations

  • Department of Mathematics, Indiana University-Purdue University Indianapolis (IUPUI), Indianapolis, USA

    Charalambos D. Aliprantis

  • Division of the Humanities and Social Sciences, CALTECH, Pasadena, USA

    Kim C. Border

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