A Utility Representation for Temporally Myopic Partial Orderings.

摘要

A utility representation for partial orders defined on a denumerably infinite programme space is obtained for the case where the partial orders satisfy a weak form of temporal myopia. Nonstandard techniques are employed, by which the space of programmes is imbedded in a hyper-linear space of *Finite dimension. The relative topology on the space of programmes induced by the product S-topology on the hyper-linear space is sufficient for the existence of a continuous linear functional in the algebraic dual of the programme space.