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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Representations of hyperharmonic cones
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by Sirkka-Liisa Eriksson PDF
Trans. Amer. Math. Soc. 305 (1988), 247-262 Request permission

Abstract:

Hyperharmonic cones are ordered convex cones possessing order properties similar to those of hyperharmonic functions on harmonic spaces. The dual of a hyperharmonic cone is defined to be the set of extended real-valued additive and left order-continuous mappings $(\not \equiv \infty )$. The second dual gives a representation of certain hyperharmonic cones in which suprema of upward directed families are pointwise suprema, although infima of pairs of functions are not generally pointwise infima. We obtain necessary and sufficient conditions for the existence of a representation of a hyperharmonic cone in which suprema of upward directed families are pointwise suprema and infima of pairs of functions are pointwise infima.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 305 (1988), 247-262
  • MSC: Primary 31D05
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0920157-2
  • MathSciNet review: 920157