 Without loss of generality, we can assume that the domain "U" of "g" is connected, as otherwise one can prove the existence of an antiderivative on each connected component.With this assumption, fix a point "z"0 in "U" and for any "z" in "U" define the function

where γ is any path joining "z"0 to "z".Such a path exists since "U" is assumed to be an open connected set.