Infinite Dimensional Analysis

1. Front Matter

   Pages i-xxii

   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. L_p-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

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.

• Analysis
• Convex Analysis
• Economic Theory
• Mathematical Analysis
• Measure Theory and Integration
• Theory of Finance
• Topology
• functional analysis
• linear optimization

• 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

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