Continuous multi-utility representations of preorders
| Autor: | Gianni Bosi, Gerhard Herden |
|---|---|
| Přispěvatelé: | Bosi, Gianni, Herden, G. |
| Rok vydání: | 2012 |
| Předmět: |
Discrete mathematics
Economics and Econometrics Multi-utility representation Specialization (pre)order Applied Mathematics Existential quantification Preorder Topological space Space (mathematics) Closed preorder Weakly continuous preorder Mathematik Isotonic Representation (mathematics) Mathematics |
| Zdroj: | Journal of Mathematical Economics. 48:212-218 |
| ISSN: | 0304-4068 |
| DOI: | 10.1016/j.jmateco.2012.05.001 |
| Popis: | Let ( X , t ) be a topological space. Then a preorder ≾ on ( X , t ) has a continuous multi-utility representation if there exists a family F of continuous and isotonic real-valued functions f on ( X , ≾ , t ) such that for all x ∈ X and all y ∈ X the inequalities x ≾ y mean that for all f ∈ F the inequalities f ( x ) ≤ f ( y ) hold. We discuss the existence of a continuous multi-utility representation by using suitable concepts of continuity of a preorder. In addition, we clarify in detail the relation between the concept of a continuous multi-utility representation and Nachbin’s concept of a normally preordered space. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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