Continuity of measurable convex and biconvex operators
HTML articles powered by AMS MathViewer
- by Lionel Thibault PDF
- Proc. Amer. Math. Soc. 90 (1984), 281-284 Request permission
Abstract:
We prove that a mapping from the product of two complete metrizable vector spaces into a topological vector space which is separately universally measurable and separately convex with respect to a convex cone is continuous.References
- J. M. Borwein, Continuity and differentiability properties of convex operators, Proc. London Math. Soc. (3) 44 (1982), no. 3, 420–444. MR 656244, DOI 10.1112/plms/s3-44.3.420
- Jens Peter Reus Christensen, Borel structures in groups and semigroups, Math. Scand. 28 (1971), 124–128. MR 308322, DOI 10.7146/math.scand.a-11010
- J. P. R. Christensen, Topology and Borel structure, North-Holland Mathematics Studies, Vol. 10, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1974. Descriptive topology and set theory with applications to functional analysis and measure theory. MR 0348724
- Pal Fischer and Zbigniew Słodkowski, Christensen zero sets and measurable convex functions, Proc. Amer. Math. Soc. 79 (1980), no. 3, 449–453. MR 567990, DOI 10.1090/S0002-9939-1980-0567990-5 J. Hoffmann-Jorgensen, The theory of analytic sets, Aarhus Universitet Danmark, various publication series, no. 10, 1970.
- Mohamed Jouak and Lionel Thibault, Equicontinuity of families of convex and concave-convex operators, Canad. J. Math. 36 (1984), no. 5, 883–898. MR 762746, DOI 10.4153/CJM-1984-050-8
- Anthony L. Peressini, Ordered topological vector spaces, Harper & Row, Publishers, New York-London, 1967. MR 0227731
- Laurent Schwartz, Sur le théorème du graphe fermé, C. R. Acad. Sci. Paris Sér. A-B 263 (1966), A602–A605 (French). MR 206676
- L. Thibault, Continuity of measurable convex multifunctions, Multifunctions and integrands (Catania, 1983) Lecture Notes in Math., vol. 1091, Springer, Berlin, 1984, pp. 216–224. MR 785588, DOI 10.1007/BFb0098814
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 281-284
- MSC: Primary 46A40
- DOI: https://doi.org/10.1090/S0002-9939-1984-0727250-X
- MathSciNet review: 727250