Positivity

, Volume 17, Issue 3, pp 459–473

Non-compact versions of Edwards’ Theorem

  • Nihat G. Gogus
  • Tony L. Perkins
  • Evgeny A. Poletsky
Article

DOI: 10.1007/s11117-012-0181-9

Cite this article as:
Gogus, N.G., Perkins, T.L. & Poletsky, E.A. Positivity (2013) 17: 459. doi:10.1007/s11117-012-0181-9

Abstract

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.

Keywords

Superlinear functionalsEnvelopesRepresenting measuresJensen measures

Mathematics Subject Classification

46A2047B6546A55

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

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