Quasi-everywhere

Summary

A property holds quasi-everywhere on a set if it holds at every point outside a set of capacity zero. It plays the role in potential theory that "almost everywhere" plays in measure theory, with capacity in place of measure. Since sets of capacity zero have Lebesgue measure zero, a property that holds quasi-everywhere also holds almost everywhere. Many results, such as Frostman's theorem and the solvability of the Dirichlet problem at boundary points, hold quasi-everywhere but not everywhere.