Utility Functions on Partially Ordered Topological Groups

Candeal-Haro, Juan Carlos; Induráin, Esteban

doi:10.2307/2159224

Cited by 3 publications

(4 citation statements)

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“…[16,17,22,38]). Indeed, in several of these situations there are theorems of automatic continuity: to put an example, any translation-invariant linear order defined on a group is continuous as regards the order topology, and a group endowed with a translationinvariant total (linear) order is actually a topological group with respect to the order topology (see [38] for further details).…”

Section: Introductionmentioning

confidence: 99%

Numerical Representability of Ordered Topological Spaces with Compatible Algebraic Structure

Candeal

Induráin

Molina

2011

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Section: Introductionmentioning

confidence: 99%

Numerical Representability of Ordered Topological Spaces with Compatible Algebraic Structure

Candeal

Induráin

Molina

2011

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“…In the crisp case, some studies on the representability of certain kinds of orderings, in terms of measure theory, have already been considered in the specialized literature 34,35,36,25,22 .…”

Section: Further Commentsmentioning

confidence: 99%

Numerical representability of fuzzy total preorders

Agud

Catalán²,

Díaz³

et al. 2012

IJCIS

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“…The aim of this paper is to generalize the results of the paper [1] to the case of locally compact groups that are not necessarily abelian. Our methods are more general and based on the concept of positive relatively (left) invariant measures.…”

Section: Introductionmentioning

confidence: 99%

“…In the paper [1], the same authors were interested in constructing continuous utility functions on a locally compact abelian group endowed with a translationinvariant, strongly continuous, and separable strict partial ordering. They used the concept of Haar measure.…”

Section: Introductionmentioning

confidence: 99%

Utility Functions Associated to Relatively Invariant Measures on Partially Ordered Locally Compact Groups

Akkouchi¹

2002

Demonstratio Mathematica

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Abstract. Let G be a topological locally compact group (abelian or not) endowed with a left Haar measure and a left translation-invariant and strongly continuous strict partial ordering -< . We consider a positive finite measure v on G, such that this order is v-separable. Then, we associate to each positive relatively invariant measure A on G a class of continuous numerical representations for the order -< . IntroductionIn Economics, the notion of utility function is a useful tool in the theory of consumption. Suppose that a society of consumers (constituted by individulas, households, tribes, etc, ...) is given and that the members of this society have an order of preferences for the products they want to choose. Then an utility function is a numerical representation of this order. It transforms preferences into numerical scales. Therefore, numerical representations of preordered sets are tools for decision making.In Mathematics, the problem of representability of complete ordering by means of a numerical function was posed long ago by Cantor (1895, 1897) (see [3] and [4]). Different studies and solutions of that problem can be found in the paper [20] of Milgram (1939) and the papers ([7, 8]) of Debreu (1954Debreu ( , 1959 or the paper of Fishburn (see [10]) in 1970.A natural extension of these ideas is the study of this problem for preorders or partial orders (not necessarily completes) in topological spaces. This study has producted a rich literature: see the works by Eilenberg (1941), Debreu (1954), Fleischer (1961 and Jaffray (1975) on completely preordered 1991 Mathematics Subject Classification: Primary 28C10, 54F05; Secondary 06F15, 90A10.

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Utility Functions on Partially Ordered Topological Groups

Abstract: Abstract.Let (X, +, x) be a locally compact abelian group endowed with a translation-invariant, strongly continuous, and separable strict partial ordering "< ." Then, there exists a continuous numerical representation for "< ." The proof leans on the concept of Haar measure.

Cited by 3 publications

References 4 publications

Numerical Representability of Ordered Topological Spaces with Compatible Algebraic Structure

Numerical Representability of Ordered Topological Spaces with Compatible Algebraic Structure

Numerical representability of fuzzy total preorders

Utility Functions Associated to Relatively Invariant Measures on Partially Ordered Locally Compact Groups

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