Hiroshima Mathematical Journal
- Hiroshima Math. J.
- Volume 38, Number 1 (2008), 37-50.
A Riesz decomposition theorem on harmonic spaces without positive potentials
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.
Hiroshima Math. J., Volume 38, Number 1 (2008), 37-50.
First available in Project Euclid: 7 April 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 31D05: Axiomatic potential theory
Secondary: 31A05: Harmonic, subharmonic, superharmonic functions
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