Continuous representability of complete preorders on the space of upper-continuous capacities

Gianni Bosi, Romano Isler

Abstract

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.


Keywords

Upper-continuous capacity; Compact metric space; Weak topology; Continuous utility function

Subject classification

06A05; 91B16

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1. Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof
G. Bosi, G.B. Mehta
Journal of Mathematical Economics  vol: 38  issue: 3  first page: 311  year: 2002  
doi: 10.1016/S0304-4068(02)00058-7



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt