Locally Solid Riesz Spaces with Applications to Economics

Locally Solid Riesz Spaces with Applications to Economics

4 (1 rating by Goodreads)

List price: US$80.00

Currently unavailable

We can notify you when this item is back in stock

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks

Description

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.
show more

Product details

  • Hardback | 344 pages
  • 184.15 x 260.35 x 25.4mm | 816.47g
  • Providence, United States
  • English
  • Revised
  • 2nd Revised edition
  • 0821834088
  • 9780821834084
  • 1,993,431

Table of contents

The lattice structure of Riesz spaces Locally solid topologies Lebesgue topologies Fatou topologies Metrizability Weak compactness in Riesz spaces Lateral completeness Market economies Solutions to the exercises Bibliography Index.
show more

Rating details

1 rating
4 out of 5 stars
5 0% (0)
4 100% (1)
3 0% (0)
2 0% (0)
1 0% (0)
Book ratings by Goodreads
Goodreads is the world's largest site for readers with over 50 million reviews. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. Close X