Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Integral type linear functionals on
ordered cones

Author: Walter Roth
Journal: Trans. Amer. Math. Soc. 348 (1996), 5065-5085
MSC (1991): Primary 46A55, 47H05
MathSciNet review: 1401784
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce linear functionals on an ordered cone that are minimal with respect to a given subcone. Using concepts developed for Choquet theory we observe that the properties of these functionals resemble those of positive Radon measures on locally compact spaces. Other applications include monotone functionals on cones of convex sets, H-integrals on H-cones in abstract potential theory, and classical Choquet theory itself.

References [Enhancements On Off] (What's this?)

  • 1. Erik M. Alfsen, Compact convex sets and boundary integrals, Springer-Verlag, New York-Heidelberg, 1971. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 57. MR 0445271
  • 2. Bernd Anger and Claude Portenier, Radon integrals, Progress in Mathematics, vol. 103, Birkhäuser Boston, Inc., Boston, MA, 1992. An abstract approach to integration and Riesz representation through function cones. MR 1138722
  • 3. Heinz Bauer, Maß- und Integrationstheorie, 2nd ed., de Gruyter Lehrbuch. [de Gruyter Textbook], Walter de Gruyter & Co., Berlin, 1992 (German). MR 1181881
  • 4. Nicu Boboc, Gheorghe Bucur, and Aurel Cornea, Order and convexity in potential theory: 𝐻-cones, Lecture Notes in Mathematics, vol. 853, Springer, Berlin, 1981. In collaboration with Herbert Höllein. MR 613980
  • 5. N. Bourbaki, Éléments de mathématique. Fasc. XIII. Livre VI: Intégration. Chapitres 1, 2, 3 et 4: Inégalités de convexité, Espaces de Riesz, Mesures sur les espaces localement compacts, Prolongement d’une mesure, Espaces 𝐿^{𝑝}, Deuxième édition revue et augmentée. Actualités Scientifiques et Industrielles, No. 1175, Hermann, Paris, 1965 (French). MR 0219684
  • 6. Benno Fuchssteiner and Wolfgang Lusky, Convex cones, North-Holland Mathematics Studies, vol. 56, North-Holland Publishing Co., Amsterdam-New York, 1981. Notas de Matemática [Mathematical Notes], 82. MR 640719
  • 7. Klaus Keimel and Walter Roth, Ordered cones and approximation, Lecture Notes in Mathematics, vol. 1517, Springer-Verlag, Berlin, 1992. MR 1176514
  • 8. Walter Roth, A new concept for a Choquet ordering, J. London Math. Soc. (2) 34 (1986), no. 1, 81–96. MR 859150,

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 46A55, 47H05

Retrieve articles in all journals with MSC (1991): 46A55, 47H05

Additional Information

Walter Roth
Affiliation: Department of Mathematics, University of Bahrain, P.O. Box 32038, Bahrain

Keywords: Locally convex cones, abstract integrals
Received by editor(s): June 27, 1994
Article copyright: © Copyright 1996 American Mathematical Society