where Ω("z") > 0. Then "f" satisfies () precisely when it is a conformal transformation from "D" equipped with this metric to the domain "D"′ equipped with the standard Euclidean metric. The function "f" is then called μ-conformal. More generally, the continuous differentiability of "f" can be replaced by the weaker condition that "f" be in the Sobolev space "W"1,2("D") of functions whose first-order distributional derivatives are in L2("D"). In this case, "f" is required to be a weak solution of (). When μ is zero almost everywhere, any homeomorphism in "W"1,2("D") that is a weak solution of () is conformal.