4 research outputs found
Sublinear and continuous order-preserving functions for noncomplete preorders
We characterize the existence of a nonnegative, sublinear and continuous
order-preserving function for a not necessarily complete preorder on a real
convex cone in an arbitrary topological real vector space. As a corollary of
the main result, we present necessary and sufficient conditions for the
existence of such an order-preserving function for a complete preorder.Comment: 8 page
Isotonies on ordered cones throught the concept of a decreasing scale
Using techniques based on decreasing scales, necessary and sufficient conditions are presented for the
existence of a continuous and homogeneous of degree one real-valued function representing a (not necessarily
complete) preorder defined on a cone of a real vector space. Applications to measure theory and expected
utility are given as consequences