Infinite Dimensional Analysis: A Hitchhiker’s Guide

✍ Scribed by Professor Charalambos D. Aliprantis, Professor Kim C. Border (auth.)

• Publisher: Springer Berlin Heidelberg
• Year: 1999
• Tongue: English
• Leaves: 691
• Category: Library

✦ Synopsis

This book is intended for the student or researcher who could benefit from functional analytic methods, but who does not have an extensive background and does not plan to make a career as a functional analyst. It develops topology, convexity, Banach lattices, integration, correspondences (multifunctions), and the analytic approach to Markov processes. Many of the results were previously available only in esoteric monographs. The choice of material was motivated from problems in control theory and economics, although the material is more applicable than applied.

✦ Table of Contents

Front Matter....Pages i-xx
Odds and ends....Pages 1-18
Topology....Pages 19-68
Metrizable spaces....Pages 69-122
Measurability....Pages 123-160
Topological vector spaces....Pages 161-236
Normed spaces....Pages 237-262
Riesz spaces....Pages 263-300
Banach lattices....Pages 301-330
Charges and measures....Pages 331-364
Measures and topology....Pages 365-394
Integrals....Pages 395-426
L p -spaces....Pages 427-454
Riesz Representation Theorems....Pages 455-472
Probability measures on metrizable spaces....Pages 473-492
Spaces of sequences....Pages 493-522
Correspondences....Pages 523-556
Measurable correspondences....Pages 557-586
Markov transitions....Pages 587-620
Ergodicity....Pages 621-633
Back Matter....Pages 635-673

✦ Subjects

Functional Analysis; Economic Theory; Applications of Mathematics; Game Theory/Mathematical Methods; Analysis; Appl.Mathematics/Computational Methods of Engineering