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Proceedings of the American Mathematical Society

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Approximately convex average sums of unbounded sets


Author: M. Ali Khan
Journal: Proc. Amer. Math. Soc. 43 (1974), 181-185
MSC: Primary 52A20; Secondary 02H25, 90A99
DOI: https://doi.org/10.1090/S0002-9939-1974-0338928-8
MathSciNet review: 0338928
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Abstract: In this note we show that the average sum of a large but finite number of unbounded and open sets is approximately convex if their ``degree of nonconvexity'' is bounded.


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

  • [1] K. J. Arrow and F. H. Hahn, General competitive analysis, Holden-Day, San Francisco, Calif., 1971. MR 0439057 (55:11958)
  • [2] D. J. Brown, Convexity of the vector average (mimeo).
  • [3] G. Debreu, Theory of value: an axiomatic analysis of economic equilibrium, Cowles Foundation for Research in Economics at Yale University, Monograph 17, Wiley, New York; Chapman & Hall, London, 1959. MR 22 #1447. MR 0110571 (22:1447)
  • [4] P. A. Loeb, A combinatorial analog of Lyapunov's theorem for infinitesimally generated atomic vector measures, Proc. Amer. Math. Soc. 39 (1973), 585-586. MR 0316674 (47:5221)
  • [5] R. M. Starr, Quasi-equilibria in markets with nonconvex preferences, Econometrica, 37 (1969), 25-38.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0338928-8
Keywords: Average sum, convex sets, unbounded, degree of nonconvexity
Article copyright: © Copyright 1974 American Mathematical Society

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