structural:reformatting
Removal of singularities

The following principle of removal of singularities holds for harmonic functions. If f is a harmonic function defined on a dotted open subset Ω ∖ { x 0 } {\displaystyle \Omega \smallsetminus \{x_{0}\}} of R n {\displaystyle \mathbb {R} ^{n}}, which is less singular at x than the fundamental solution (for n > 2), that is f (x) = o (| x − x 0 | 2 − n), as x → x 0, {\displaystyle f(x)=o\left(\vert x-x_{0}\vert ^{2-n}\right),\qquad {\text{as }}x\to x_{0},} then f extends to a harmonic function on Ω (compare Riemann's theorem for functions of a complex variable).