Infinite Dimensional Analysis

1. Front Matter

   Pages i-xx

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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

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.

• Algebra
• Convexity
• Markov
• Theory of Finance
• Topologie
• Wirtschaftstheorie
• calculus
• compactness
• duality
• integration
• linear optimization
• mathematical analysis
• measure
• operator
• step function

• 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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