Ebook: Infinite Dimensional Analysis: A Hitchhiker’s Guide
- Tags: Economic Theory, Functional Analysis, Game Theory/Mathematical Methods
- Year: 2006
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 3
- Language: English
- pdf
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.
Aimed at students and researchers, this is the very first book to present functional analysis in a unified manner, along with applications to economics, social sciences, and engineering.
What readers will find in this monograph is nothing less than a complete and rigorous study of modern functional analysis.
It is intended for the student or researcher who could benefit from functional analytic methods, but who does not have an extensive background in the subject and does not plan to make a career as a functional analyst.
It develops the topological structures in connection with measure theory, convexity, Banach lattices, integration, correspondences (multifunctions), and the analytic approach to Markov processes.
Many of the results were previously available only in works scattered throughout the literature, and the choice of material has been predicated on problems in control theory and economics. Included is lots of new and important material as well as additional applications.
Aimed at students and researchers, this is the very first book to present functional analysis in a unified manner, along with applications to economics, social sciences, and engineering.
What readers will find in this monograph is nothing less than a complete and rigorous study of modern functional analysis.
It is intended for the student or researcher who could benefit from functional analytic methods, but who does not have an extensive background in the subject and does not plan to make a career as a functional analyst.
It develops the topological structures in connection with measure theory, convexity, Banach lattices, integration, correspondences (multifunctions), and the analytic approach to Markov processes.
Many of the results were previously available only in works scattered throughout the literature, and the choice of material has been predicated on problems in control theory and economics. Included is lots of new and important material as well as additional applications.
Content:
Front Matter....Pages i-xxii
Odds and ends....Pages 1-20
Topology....Pages 21-67
Metrizable spaces....Pages 69-126
Measurability....Pages 127-161
Topological vector spaces....Pages 163-224
Normed spaces....Pages 225-250
Convexity....Pages 251-309
Riesz spaces....Pages 311-345
Banach lattices....Pages 347-370
Charges and measures....Pages 371-402
Integrals....Pages 403-432
Measures and topology....Pages 433-460
L p-spaces....Pages 461-486
Riesz Representation Theorems....Pages 487-503
Probability measures....Pages 505-523
Spaces of sequences....Pages 525-554
Correspondences....Pages 555-590
Measurable correspondences....Pages 591-620
Markov transitions....Pages 621-653
Ergodicity....Pages 655-666
Back Matter....Pages 667-705
Aimed at students and researchers, this is the very first book to present functional analysis in a unified manner, along with applications to economics, social sciences, and engineering.
What readers will find in this monograph is nothing less than a complete and rigorous study of modern functional analysis.
It is intended for the student or researcher who could benefit from functional analytic methods, but who does not have an extensive background in the subject and does not plan to make a career as a functional analyst.
It develops the topological structures in connection with measure theory, convexity, Banach lattices, integration, correspondences (multifunctions), and the analytic approach to Markov processes.
Many of the results were previously available only in works scattered throughout the literature, and the choice of material has been predicated on problems in control theory and economics. Included is lots of new and important material as well as additional applications.
Content:
Front Matter....Pages i-xxii
Odds and ends....Pages 1-20
Topology....Pages 21-67
Metrizable spaces....Pages 69-126
Measurability....Pages 127-161
Topological vector spaces....Pages 163-224
Normed spaces....Pages 225-250
Convexity....Pages 251-309
Riesz spaces....Pages 311-345
Banach lattices....Pages 347-370
Charges and measures....Pages 371-402
Integrals....Pages 403-432
Measures and topology....Pages 433-460
L p-spaces....Pages 461-486
Riesz Representation Theorems....Pages 487-503
Probability measures....Pages 505-523
Spaces of sequences....Pages 525-554
Correspondences....Pages 555-590
Measurable correspondences....Pages 591-620
Markov transitions....Pages 621-653
Ergodicity....Pages 655-666
Back Matter....Pages 667-705
....