[PDF][PDF] Representations of an interval order by means of two upper semicontinuous functions
A pair (u, v) of real-valued functions on a set X is said to represent an interval order≼ on X if
x≼ y is equivalent to u (x)≤ v (y) for all x, y∈ X. In this paper we provide a characterization of
the existence of a pair (u, v) of upper semicontinuous real-valued functions representing an
interval order≼ on a topological space (X, τ). The famous Rader's utility representation
theorem appears as a corollary of our main result.
x≼ y is equivalent to u (x)≤ v (y) for all x, y∈ X. In this paper we provide a characterization of
the existence of a pair (u, v) of upper semicontinuous real-valued functions representing an
interval order≼ on a topological space (X, τ). The famous Rader's utility representation
theorem appears as a corollary of our main result.
Abstract
A pair (u, v) of real-valued functions on a set X is said to represent an interval order≼ on X if x≼ y is equivalent to u (x)≤ v (y) for all x, y∈ X. In this paper we provide a characterization of the existence of a pair (u, v) of upper semicontinuous real-valued functions representing an interval order≼ on a topological space (X, τ). The famous Rader’s utility representation theorem appears as a corollary of our main result.
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