Polysuperharmonic functions on a harmonic space

In the context of the axiomatic potential theory, we introduce the notions of polyharnionic functions and polypotentials on a Brelot harmonic space Ω. For these functions, we prove some results analogous to the Riesz decomposition, balayage, domination principle, etc., which are usually associated with harmonic and superharmonic functions on Ω. We also consider the polyharmonic classifications of the harmonic spaces.