Infinite Dimensional Analysis

What you'll 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 a number of topic areas such as measure theory, convexity, and Banach lattices, as well as covering the analytic approach to Markov processes. Many of the results were previously available only in works scattered throughout the literature.

"This monograph presents 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 does not have an extensive background 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. The choice of material was motivated from problems in control theory and economics, although the material is more applicable than applied. TOC:A foreword to the practical.- Odds and ends.- Topology.- Metrizable spaces.- Measurability.- Topological vector spaces.- Normed spaces.- Convexity.- Riesz spaces.- Banach lattices.- Charges and measures.- Integrals.- Measures and topology.- Lp-spaces.- Riesz Representation Theorems.- Probability measures.- Spaces of sequences.- Correspondences.- Measurable correspondences.- Markov transitions.- Ergodicity."

Odds and ends.- Topology.- Metrizable spaces.- Measurability.- Topological vector spaces.- Normed spaces.- Convexity.- Riesz spaces.- Banach lattices.- Charges and measures.- Integrals.- Measures and topology.- Lp-spaces.- Riesz Representation Theorems.- Probability measures.- Spaces of sequences.- Correspondences.- Measurable correspondences.- Markov transitions.- Ergodicity.