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A Choquet-Deny theorem for affine functions on a Choquet simplex

Published online by Cambridge University Press:  20 January 2009

H. A. Priestley
H. A. Priestley
Affiliation:
Mathematical Institute, 24–29 St GilesOxford(England)
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The closed wedges in C(X) (the space of real continuous functions on a compact Hausdorff space X) which are also inf-lattices have been characterized by Choquet and Deny (2); see also (5). The present note extends their result to certain wedges of affine continuous functions on a Choquet simplex, the generalization being in the same spirit as the generalization of the Kakutani- Stone theorem obtained by Edwards in (4).

I should like to thank my supervisor, Dr D. A. Edwards, for suggesting this problem and for his subsequent help. I am also grateful to the referee for correcting several slips.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 4 , December 1969 , pp. 325 - 327
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

REFERENCES

(1) Bauer, H. Cones convexes semi-ré;ticulés de fonctions continues; théorémes de représentation et de stabilité, Séminaire Brelot-Choquet-Deny, 8e année, exposé n° 5, Paris (1965).Google Scholar
(2) Choquet, G. and Deny, J.Ensembles semi-réticulés et ensembles réticulés de fonctions continues, J. Math. Pures Appl. (9) 36 (1957), 179–189.Google Scholar
(3) Edwards, D. A.Minimum-stable wedges of semi-continuous functions, Math. Scand. 19 (1966), 15–26.CrossRefGoogle Scholar
(4) Edwards, D. A.On uniform approximation of affine functions on a compact convex set, Quart. J. Math. Oxford (2) 20 (1969), 139–142.CrossRefGoogle Scholar
(5) Nachbin, L.Elements of approximation theory (Van Nostrand Mathematical Studies No. 14, Princeton N.J., 1966).Google Scholar