  The level of a function f on an n-dimensional space encloses a region. The
volume of a region between two such levels depends on both levels. Fixing one
of them the volume becomes a function of the remaining level. We show that if
the function f is smooth, the volume function is again smooth for regular
values of f. For critical values of f the volume function is only finitely
differentiable. The initial motivation for this study comes from Radiotherapy,
where such volume functions are used in an optimization process. Thus their
differentiability properties become important.
