Hiroshima Mathematical Journal

A Riesz decomposition theorem on harmonic spaces without positive potentials

I. Bajunaid, J. M. Cohen, F. Colonna, and D. Singman

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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.

Article information

Hiroshima Math. J., Volume 38, Number 1 (2008), 37-50.

First available in Project Euclid: 7 April 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 31D05: Axiomatic potential theory
Secondary: 31A05: Harmonic, subharmonic, superharmonic functions

harmonic space superharmonic flux


Bajunaid, I.; Cohen, J. M.; Colonna, F.; Singman, D. A Riesz decomposition theorem on harmonic spaces without positive potentials. Hiroshima Math. J. 38 (2008), no. 1, 37--50. doi:10.32917/hmj/1207580344. https://projecteuclid.org/euclid.hmj/1207580344

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