By the mean value theorem for triple integrals,

for some point in the closed bounded region , where is a smooth vector field in a domain that includes along with its boundary and is the volume of the region Then, by the divergence theorem, if is the surface bounding the region and is orientable , then

Let be a fixed point in the region and we apply the above discussion to the region a small sphere centered at the point of radius Then, there exists a point such that
             
             Figure: Sphere at inside