Representations of Preferences Orderings

Douglas S. Bridges, Ghanshyam B. Mehta (auth.)3540588396, 9783540588399, 0387588396, 9780387588391

This monograph is devoted to a rigorous presentation of results about the representation of preference orderings by real-valued order isomorphisms (“utility functions”). The authors have gathered together, from sources scattered throughout a wide range of the literature of mathematics and economics, the most significant theorems and methods in their field. The book will be a valuable resource for theoretical economists, mathematicians, and all interested in partial orders and their representation. It could also be used as the text for an advanced graduate course in mathematical economics.

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Table of contents :
Front Matter….Pages i-x
Ordered Sets and Order Homomorphisms….Pages 1-25
Order Homomorphisms in Euclidean Space….Pages 27-35
The Fundamental Theorems….Pages 37-48
A Miscellany of Representations….Pages 49-71
The Urysohn-Nachbin Approach….Pages 73-86
Interval Orders….Pages 87-108
Differentiable Order Homomorphisms….Pages 109-124
Jointly Continuous Order Homomorphisms….Pages 125-146
Back Matter….Pages 147-165