Locally Solid Riesz Spaces with Applications to Economics (Mathematical Surverys and Monographs Series) / Edition 2

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Overview

Riesz space (or a vector lattice) is an ordered vector space that is simultaneously a lattice. A topological Riesz space (also called a locally solid Riesz space) is a Riesz space equipped with a linear topology that has a base consisting of solid sets. Riesz spaces and ordered vector spaces play an important role in analysis and optimization. They also provide the natural framework for any modern theory of integration. This monograph is the revised edition of the authors' book Locally Solid Riesz Spaces (1978, Academic Press). It presents an extensive and detailed study (with complete proofs) of topological Riesz spaces. The book starts with a comprehensive exposition of the algebraic and lattice properties of Riesz spaces and the basic properties of order bounded operators between Riesz spaces. Subsequently, it introduces and studies locally solid topologies on Riesz spaces— the main link between order and topology used in this monograph. Special attention is paid to several continuity properties relating the order and topological structures of Riesz spaces, the most important of which are the Lebesgue and Fatou properties. A new chapter presents some surprising applications of topological Riesz spaces to economics. In particular, it demonstrates that the existence of economic equilibria and the supportability of optimal allocations by prices in the classical economic models can be proven easily using techniques from the theory of topological Riesz spaces. At the end of each chapter there are exercises that complement and supplement the material in the chapter. The last chapter of the book presents complete solutions to all exercises. Prerequisites are the fundamentals of real analysis, measure theory, and functional analysis. This monograph will be useful to researchers and graduate students in mathematics. It will also be an important reference tool to mathematical economists and to all scientists and engineers who use order structures in their research.

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Product Details

  • ISBN-13: 9780821834084
  • Publisher: American Mathematical Society
  • Publication date: 11/1/2003
  • Series: Mathematical Surveys and Monographs , #105
  • Edition number: 2
  • Pages: 360
  • Product dimensions: 7.20 (w) x 10.28 (h) x 0.91 (d)

Table of Contents

Preface of the 1[superscript st] Edition
Preface of the 2[superscript st] Edition
List of Special Symbols
Ch. 1 The Lattice Structure of Riesz spaces 1
Ch. 2 Locally Solid Topologies 49
Ch. 3 Lebesgue Topologies 75
Ch. 4 Fatou Topologies 99
Ch. 5 Metrizability 119
Ch. 6 Weak Compactness in Riesz Spaces 143
Ch. 7 Lateral Completeness 179
Ch. 8 Market Economies 215
Ch. 9 Solutions to the Exercises 267
Bibliography 331
Index 337
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