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Locally Solid Riesz Spaces with Applications to Economics (Hardcover, 2nd Revised edition)
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Locally Solid Riesz Spaces with Applications to Economics (Hardcover, 2nd Revised edition)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 17 working days
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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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