Fine Topology (potential Theory)

Fine Topology (potential Theory)

In mathematics, in the field of potential theory, the fine topology is a natural topology for setting the study of subharmonic functions. In the earliest studies of subharmonic functions, only smooth functions were considered, namely those for which where is the Laplacian. In that case it was natural to consider only the Euclidean topology, but with the advent of upper semi-continuous subharmonic functions introduced by F. Riesz, the fine topology became the more natural tool in many situations.