Integral type linear functionals on ordered cones

Roth, Walter

doi:10.1090/S0002-9947-96-01858-2

Integral type linear functionals on ordered cones
HTML articles powered by AMS MathViewer

by Walter Roth PDF

Trans. Amer. Math. Soc. 348 (1996), 5065-5085 Request permission

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

Erik M. Alfsen, Compact convex sets and boundary integrals, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 57, Springer-Verlag, New York-Heidelberg, 1971. MR 0445271, DOI 10.1007/978-3-642-65009-3
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, DOI 10.1007/978-1-4612-0377-3
Heinz Bauer, Maß- und Integrationstheorie, 2nd ed., de Gruyter Lehrbuch. [de Gruyter Textbook], Walter de Gruyter & Co., Berlin, 1992 (German). MR 1181881, DOI 10.1515/9783110871739
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, DOI 10.1007/BFb0090447
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 $L^{p}$, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1175, Hermann, Paris, 1965 (French). Deuxième édition revue et augmentée. MR 0219684
Benno Fuchssteiner and Wolfgang Lusky, Convex cones, Notas de Matemática [Mathematical Notes], vol. 82, North-Holland Publishing Co., Amsterdam-New York, 1981. MR 640719
Klaus Keimel and Walter Roth, Ordered cones and approximation, Lecture Notes in Mathematics, vol. 1517, Springer-Verlag, Berlin, 1992. MR 1176514, DOI 10.1007/BFb0089190
Walter Roth, A new concept for a Choquet ordering, J. London Math. Soc. (2) 34 (1986), no. 1, 81–96. MR 859150, DOI 10.1112/jlms/s2-34.1.81