, Volume 17, Issue 3, pp 459–473 | Cite as

Non-compact versions of Edwards’ Theorem

  • Nihat G. Gogus
  • Tony L. Perkins
  • Evgeny A. PoletskyEmail author


Edwards’ Theorem establishes duality between a convex cone in the space of continuous functions on a compact space X and the set of representing or Jensen measures for this cone. It is a direct consequence of the description of positive superlinear functionals on C(X). In this paper we obtain the description of such functionals when X is a locally compact σ-compact Hausdorff space. As a consequence we prove non-compact versions of Edwards’ Theorem.


Superlinear functionals Envelopes Representing measures Jensen measures 

Mathematics Subject Classification

46A20 47B65 46A55 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aliprantis C.D., Border K.C.: Infinite Dimensional Analysis 3rd edn. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  2. 2.
    Aliprantis C.D., Tourky R.: Cones and Duality. Graduate Studies in Mathematics, 84. American Mathematical Society, Providence (2007)Google Scholar
  3. 3.
    Edwards, D.A.: Choquet boundary theory for certain spaces of lower semicontinuous functions, in function algebras. In: Proceedings of the international symposium on function algebras, Chicago, pp. 300–309Google Scholar
  4. 4.
    Gogus N.G.: Continuity of plurisubharmonic envelopes. Ann. Polon. Math. 86, 197–217 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Gamelin Th.: Uniform algebras and Jensen measures. Cambridge University Press, Cambridge (1978)zbMATHGoogle Scholar
  6. 6.
    Hörmander L.: Sur la fonction d’appui des ensembles convexes dans un espace localement convexe. Ark. Mat. 3, 181–186 (1955)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Poletsky E.A.: Plurisubharmonic functions as solutions of variational problems. Proc. Sympos. Pure Math. 52(Part 1), 163–171 (1991)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Rubinov A.M.: Sublinear operators and their applications. Uspehi Mat. Nauk. 32, 113–174 (1977)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Wikström F.: Jensen measures and boundary values of plurisubharmonic functions. Ark. Mat. 39, 181–200 (2001)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Nihat G. Gogus
    • 1
  • Tony L. Perkins
    • 2
  • Evgeny A. Poletsky
    • 2
    Email author
  1. 1.Faculty of Engineering and Natural SciencesSabanci UniversityOrhanli, TuzlaTurkey
  2. 2.Department of MathematicsSyracuse UniversitySyracuseUSA

Personalised recommendations