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Utility functions on partially ordered topological groups


Authors: Juan Carlos Candeal-Haro and Esteban Induráin Eraso
Journal: Proc. Amer. Math. Soc. 115 (1992), 765-767
MSC: Primary 90A10; Secondary 06F15, 28C10, 54F05
DOI: https://doi.org/10.1090/S0002-9939-1992-1116255-X
MathSciNet review: 1116255
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] G. Cantor, Beiträge zur Begründung der transfinite Mengenlehre I, Math. Ann. 46 (1895), 481-512.
  • [2] -, Beiträge zur Begründung der transfinite Mengenlehre II, Math. Ann. 49 (1897), 207-246. MR 1510964
  • [3] -, Spaces of economic agents, J. Econom. Theory 15 (1977), 160-173. MR 0496461 (58:14999)
  • [4] G. Chichilnisky, Continuous representations of preferences, Rev. Econom. Stud. 47 (1980), 959-963. MR 611121 (83a:90011)
  • [5] S. Eilenberg, Ordered topological spaces, Amer. J. Math. 63 (1941), 39-45. MR 0003201 (2:179e)
  • [6] P. C. Fishburn, Utility theory for decision making, John Wiley, New York, 1970. MR 0264810 (41:9401)
  • [7] G. Herden, On the existence of utility functions I, Math. Social Sci. 17 (1989), 297-313. MR 1006181 (91c:90011)
  • [8] -, On the existence of utility functions II, Math. Social Sci. 18 (1989), 107-117. MR 1016502 (91c:90012)
  • [9] G. Mehta, Continuous utility functions, Econom. Lett. 18 (1985), 113-115. MR 810927 (86m:90024)
  • [10] -, Existence of an order-preserving function on normally preordered spaces, Bull. Austral. Math. Soc. 34 (1986), 141-147. MR 847982 (87h:54061)
  • [11] K. R. Mount and S. Reiter, Construction of a continuous utility function for a class of preferences, J. Math. Econom. 3 (1976), 227-245. MR 0429048 (55:2068)
  • [12] L. Nachbin,Topologia e ordem, Univ. of Chicago Press, 1950.
  • [13] W. Neuefeind, On continuous utility, J. Econom. Theory 5 (1972), 174-176. MR 0449501 (56:7803)
  • [14] B. Peleg, Utility functions for partially ordered topological spaces, Econometrica 38 (1970), 93-96. MR 0281166 (43:6885)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1116255-X
Keywords: Topological group, translation-invariant partial ordering, Haar measure, utility function
Article copyright: © Copyright 1992 American Mathematical Society

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