An important theorem in vector calculus accredited to Karl Friedrich Gauss. It states, in its generality:

∫∫F dS =

S

^ (double integral over S)

∫∫∫div F dV

E

^ (triple integral over E)

Where E is the volume enclosed by the surface S and div F is the divergence of F, of course.

The formula is a generalization of Green's and Stokes' theorems.

It is also referred to as the Divergence Theorem (because of div F) and Ostrogradsky's Theorem, after another mathematician who discovered the formula independant of Gauss.