What is 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, namely those for which Δ u ≥ 0 , {\displaystyle \Delta u\geq 0,} where Δ {\displaystyle \Delta } is the Laplacian, only smooth functions were considered. 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.