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Representation of strongly independent preorders by sets of scalar-valued functions

McCarthy, David and Mikkola, Kalle and Thomas, Teruji (2017): Representation of strongly independent preorders by sets of scalar-valued functions.

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Abstract

We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infinite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfies a condition that we call Polarization.

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