# Balayage

In modern terms, the balayage operator maps a measure μ on a closed domain D to a measure ν on the boundary ∂ D, so that the Newtonian potentials of μ and ν coincide outside ${\displaystyle {\bar {D}}}$. The procedure is called balayage since the mass is "swept out" from D onto the boundary.
${\displaystyle f(x)=\int _{\partial D}f(y)\,d\nu _{x}(y).}$