Balayage

Summary

Balayage, French for "sweeping out", replaces a measure by a measure on a given set. The new measure has the same potential as the old one outside that set, and on it up to small exceptional sets. Poincaré introduced it to solve the Dirichlet problem: the charge of a measure in a domain is swept to the boundary through harmonic measure. In modern potential theory the balayage of a measure onto any set is defined through the reduced function of its potential. It is one of the basic operations of classical and axiomatic potential theory.