Utility functions on partially ordered topological groups

Candeal-Haro, Juan Carlos; Induráin Eraso, Esteban

doi:10.1090/S0002-9939-1992-1116255-X

Utility functions on partially ordered topological groups
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by Juan Carlos Candeal-Haro and Esteban Induráin Eraso

Proc. Amer. Math. Soc. 115 (1992), 765-767

DOI: https://doi.org/10.1090/S0002-9939-1992-1116255-X

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Abstract:

Let $(X, + ,\tau )$ 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.

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