Balayage space

Summary

A balayage space is a locally compact space with a countable base together with a convex cone of positive lower semicontinuous functions. This cone plays the role of the positive superharmonic functions. The axioms are chosen so that balayage, the sweeping of functions and measures onto sets, can be carried out. The notion was developed by Jürgen Bliedtner and Wolfhard Hansen as a common frame for harmonic spaces and for the potential theory of Markov processes. Its theory includes the fine topology, thin sets, and the Dirichlet problem.