Lebesgue points and the fundamental convergence theorem for superharmonic functions on metric spaces
The authors provide a new proof for the fundamental convergence theorem for superharmonic functions on metric measure spaces. The theorem states that a regularized infimum of superharmonic functions is a superharmonic function. They also provide a new proof for the fact that Newtonian functions have Lebesgue points outside a set of capacity zero, and give a sharp result on when superharmonic functions have \(L^q\)-Lebesgue points everywhere.
scientific article; zbMATH DE number 5708819
scientific article