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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Measurability of lattice operations in a cone
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by Kohur Gowrisankaran PDF
Proc. Amer. Math. Soc. 41 (1973), 237-240 Request permission

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
  • 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
  • J. L. Kelley and Isaac Namioka, Linear topological spaces, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. 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. MR 0166578
  • Anthony L. Peressini, Ordered topological vector spaces, Harper & Row, Publishers, New York-London, 1967. MR 0227731
  • Helmut H. Schaefer, Topological vector spaces, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0193469
  • Laurent Schwartz, Radon measures on arbitrary topological spaces and cylindrical measures, Tata Institute of Fundamental Research Studies in Mathematics, No. 6, Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London, 1973. MR 0426084
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 41 (1973), 237-240
  • MSC: Primary 46A40
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0346479-9
  • MathSciNet review: 0346479