  In this paper we prove the rectifiability of and measure bounds on the
singular set of the free boundary for minimizers of a functional first
considered by Alt-Caffarelli. Our main tools are the Quantitative
Stratification and Rectifiable-Reifenberg framework of Naber-Valtorta, which
allow us to do a type of "effective dimension-reduction." The arguments are
sufficiently robust that they apply to a broad class of related free boundary
problems as well.
