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Transactions of the American Mathematical Society

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Representations of hyperharmonic cones


Author: Sirkka-Liisa Eriksson
Journal: Trans. Amer. Math. Soc. 305 (1988), 247-262
MSC: Primary 31D05
MathSciNet review: 920157
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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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DOI: https://doi.org/10.1090/S0002-9947-1988-0920157-2
Article copyright: © Copyright 1988 American Mathematical Society