Extending Utility Representations of Partial Orders

Details Extending Utility Representations of Partial Orders Extending Utility Representations of Partial Orders

2005-08-11

arxiv.org/abs/math/0508199v1

Mathematics

Optimization and Control

15 pages

Scientific paper

The problem is considered as to whether a monotone function defined on a subset P of a Euclidean space can be strictly monotonically extended to the whole space. It is proved that this is the case if and only if the function is {\em separably increasing}. Explicit formulas are given for a class of extensions which involves an arbitrary bounded increasing function. Similar results are obtained for monotone functions that represent strict partial orders on arbitrary abstract sets X. The special case where P is a Pareto subset is considered.

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