  We consider constraints on the measure of the support for integrable
functions on arbitrary measure spaces. It is shown that this non-convex and
discontinuous constraint can be equivalently reformulated by the difference of
two convex and continuous functions, namely the $L^1$-norm and the so-called
largest-$K$-norm. The largest-$K$-norm is studied and its convex
subdifferential is derived. An exemplary problem is solved by applying a DC
method to the reformulated problem.
