Continuous representability of complete preorders on the space of upper-continuous capacities
Keywords:Upper-continuous capacity, Compact metric space, Weak topology, Continuous utility function
Given a compact metric space (X, d), and its Borel σ-algebra Σ, we discuss the existence of a (semi)continuous utility function U for a complete preorder ≤ on a subset M’(X) of the space M(X) of all upper-continuous capacities on Σ, endowed with the weak topology.
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