Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Measurability of lattice operations in a cone

Author: Kohur Gowrisankaran
Journal: Proc. Amer. Math. Soc. 41 (1973), 237-240
MSC: Primary 46A40
MathSciNet review: 0346479
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ be a locally convex Hausdorff topological vector space and $ C$ a convex cone generating $ X$ such that $ C$ is a lattice in its own order. Under suitable conditions $ (x,y) \to \sup (x,y)$ and $ \inf (x,y)$ are shown to be measurable mappings.

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

  • [1] Kohur Gowrisankaran, Integral representation for a class of multiply superharmonic functions, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 4, 105–143 (English, with French summary). MR 335838
  • [2] J. L. Kelley and Isaac Namioka, Linear topological spaces, With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. MR 0166578
  • [3] Anthony L. Peressini, Ordered topological vector spaces, Harper & Row, Publishers, New York-London, 1967. MR 0227731
  • [4] Helmut H. Schaefer, Topological vector spaces, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1966. MR 0193469
  • [5] Laurent Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London, 1973. Tata Institute of Fundamental Research Studies in Mathematics, No. 6. MR 0426084

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A40

Retrieve articles in all journals with MSC: 46A40

Additional Information

Keywords: Ordered vector space, cone, lattice, compact base, Borel function
Article copyright: © Copyright 1973 American Mathematical Society