A Weierstrass-Stone theorem for Choquet simplexes

David Alan Edwards; G. F. Vincent-Smith

Annales de l'institut Fourier (1968)

  • Volume: 18, Issue: 1, page 261-282
  • ISSN: 0373-0956

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Edwards, David Alan, and Vincent-Smith, G. F.. "A Weierstrass-Stone theorem for Choquet simplexes." Annales de l'institut Fourier 18.1 (1968): 261-282. <http://eudml.org/doc/73946>.

@article{Edwards1968,
author = {Edwards, David Alan, Vincent-Smith, G. F.},
journal = {Annales de l'institut Fourier},
keywords = {functional analysis},
language = {eng},
number = {1},
pages = {261-282},
publisher = {Association des Annales de l'Institut Fourier},
title = {A Weierstrass-Stone theorem for Choquet simplexes},
url = {http://eudml.org/doc/73946},
volume = {18},
year = {1968},
}

TY - JOUR
AU - Edwards, David Alan
AU - Vincent-Smith, G. F.
TI - A Weierstrass-Stone theorem for Choquet simplexes
JO - Annales de l'institut Fourier
PY - 1968
PB - Association des Annales de l'Institut Fourier
VL - 18
IS - 1
SP - 261
EP - 282
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/73946
ER -

References

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  1. [1] T. ANDÔ, On fundamental properties of a Banach space with a cone, Pacific Journ. Math., 12 (1962), 1163-1169. Zbl0123.30802MR27 #568
  2. [2] H. BAUER, Minimalstellen von Funktionen und Extremalpunkte II, Arch. Math. 11 (1960), 200-205. Zbl0098.08003MR24 #A251
  3. [3] H. BAUER, Konvexität in topologischen Vektorräumen, Xerographed lecture notes, Hamburg 1963/1964. 
  4. [4] E. BISHOP and K. DE LEEUW, The representation of linear functionals by measures on sets of extreme points, Ann. Inst. Fourier, Grenoble, 11 (1961), 89-136. 
  5. [5] N. BOURBAKI, Intégration (Chapitres 1-4), 2ième édition, Hermann, Paris 1965. Zbl0136.03404
  6. [6] G. CHOQUET and P.-A. MEYER, Existence et unicité des représentations intégrales dans les convexes compacts quelconques, Ann. Inst. Fourier, Grenoble, 13 (1963), 139-154. Zbl0122.34602MR26 #6748
  7. [7] D.A. EDWARDS, The homeomorphic affine embedding of a locally compact cone into a Banach dual space endowed with the vague topology, Proc. Lond. Math. Soc. 14 (1964), 399-414. Zbl0205.12202MR29 #6274
  8. [8] D.A. EDWARDS, Séparation des fonctions réelles définies sur un simplexe de Choquet, C.R. Acad. Sci. Paris 261 (1965), 2798-2800. Zbl0156.13301MR32 #8131
  9. [9] D.A. EDWARDS, On separation and approximation of real functions defined on a Choquet simplex, Proc. Second Prague Topological Symposium (1966), 122-128. Zbl0177.16302
  10. [10] D.A. EDWARDS, The affine continuous functions on a Choquet simplex, Proc. Bruges Summer School on Topological Algebra Theory (1966), Brussels 1967. Zbl0184.34401
  11. [11] E.G. EFFROS, Structure in simplexes, Acta Math. 117 (1967), 103-121. Zbl0154.14201MR34 #3287
  12. [12] S. KAKUTANI, Concrete representation of abstract (M)-spaces, Ann. of Math. 42 (1941), 994-1024. Zbl0060.26604
  13. [13] J. LINDENSTRAUSS, Extension of compact operators, Mem. Amer. Math. Soc. 48, Providence, R.I., (1964). Zbl0141.12001MR31 #3828
  14. [14] P.-A. MEYER, Probabilités et potentiel, Hermann, Paris, (1966). Zbl0138.10402MR34 #5118
  15. [15] R.R. PHELPS, Lectures on Choquet's theorem, van Nostrand, Princeton N.J., 1966. Zbl0135.36203MR33 #1690
  16. [16] F. RIESZ, Sur quelques notions fondamentales dans la théorie générale des opérations linéaires, Ann. of Math. 41 (1940), 174-206. Zbl0022.31802MR1,147dJFM66.0553.01

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