References
R. J. Aumann, Utility theory without the completeness axiom. Econometrica30, 445–462 (1962). (Correction in Econometrica32, 210–212 (1964)).
G.Birkhoff, Lattice Theory. American Mathematical Society, Providence, R.I. 1948.
P. C.Fishburn, Utility Theory for Decision Making. New York 1970.
P. C. Fishburn, A study of lexicographic expected utility. Management Sci.17, 672–678 (1971).
P. C. Hammer, Maximal convex sets. Duke Math. J.22, 103–106 (1955).
M.Hausner, Multidimensional utilities. In: Decision Processes, R. M. Thrall et al., eds., 167–180. New York 1954.
M. Hausner andJ. G. Wendel, Ordered vector spaces. Proc. Amer. Math. Soc.3, 977–982 (1952).
Y. Kannai, Existence of a utility in infinite dimensional partially ordered spaces. Israel J. Math.1, 229–234 (1963).
V. Klee, Separation properties of convex cones. Proc. Amer. Math. Soc.6, 313–318 (1955).
V. Klee, Boundedness and continuity of linear functionals. Duke Math. J.22, 263–270 (1955).
V. Klee, The structure of semispaces. Math. Scand.4, 54–64 (1956).
V. Klee, Utility functions and the ‘lin’ operation for convex sets. Israel J. Math.2, 191–197 (1964).
C. E. Moore, Concrete semispaces and lexicographic separation of convex sets. Pacific J. Math.44, 659–670 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Klee, V., Maluta, E. & Zanco, C. Archimedean levels, semispaces, and majorization of convex cones. Arch. Math 61, 250–256 (1993). https://doi.org/10.1007/BF01198721
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01198721