대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제43권4호
  • /
  • Pages.861-868
  • /
  • 2006
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A NOTE ON A CHOQUET-DENY-TYPE THEOREM

  • 발행 : 2006.11.30
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초록

We present a Choquet-Deny-type theorem for downward filtering convex sets of continuous functions and show that the Identity Korovkin cone of a downward filtering convex cone S is exactly the uniform closure of S.

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참고문헌

  1. G. Choquet and J. Deny, Ensembles semi-reticules et ensembles reticules de fonctions continues, J. Math. Pures Appl. (9) 36 (1957), 179-189
  2. H. O. Flosser, R. Irmisch, and W. Roth, Infimum-stable convex cones and approx-imation, Proc. London Math. Soc. (3) 42 (1981), no. 1, 104-120
  3. L. Nachbin, Topology and order, Van Nostrand, Princeton, NJ, 1965; reprinted by Krieger, Huntington, NY, 1976
  4. L. Nachbin, Elements of Approximation Theory, Van Nostrand, Princeton, NJ, 1967; reprinted by Krieger, Huntington, N. Y., 1976
  5. H. A. Priestley, A Choquet-Deny theorem for affine functions on a Choquet simplex, Proc. Edinburgh Math. Soc. (2) 16 (1968), 325-327
  6. J. B. Prolla, The uniform closure of convex semi-lattices, Approximation, probability and related fields, 413-421, Plenum, New York, 1994