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March 2008 A Riesz decomposition theorem on harmonic spaces without positive potentials
I. Bajunaid, J. M. Cohen, F. Colonna, D. Singman
Hiroshima Math. J. 38(1): 37-50 (March 2008). DOI: 10.32917/hmj/1207580344


In this paper, we give a new definition of the flux of a superharmonic function defined outside a compact set in a Brelot space without positive potentials. We also give a new notion of potential in a BS space (that is, a harmonic space without positive potentials containing the constants) which leads to a Riesz decomposition theorem for the class of superharmonic functions that have a harmonic minorant outside a compact set. Furthermore, we give a characterization of the local axiom of proportionality in terms of a global condition on the space.


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I. Bajunaid. J. M. Cohen. F. Colonna. D. Singman. "A Riesz decomposition theorem on harmonic spaces without positive potentials." Hiroshima Math. J. 38 (1) 37 - 50, March 2008.


Published: March 2008
First available in Project Euclid: 7 April 2008

zbMATH: 1181.05055
MathSciNet: MR2397379
Digital Object Identifier: 10.32917/hmj/1207580344

Primary: 31D05
Secondary: 31A05

Rights: Copyright © 2008 Hiroshima University, Mathematics Program


Vol.38 • No. 1 • March 2008
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