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.
"A Riesz decomposition theorem on harmonic spaces without positive potentials." Hiroshima Math. J. 38 (1) 37 - 50, March 2008. https://doi.org/10.32917/hmj/1207580344