  The Chermak-Delgado measure of a finite group is a function which assigns to
each subgroup a positive integer. In this paper, we give necessary and
sufficient conditions for when the Chermak-Delgado measure of a group is
actually a map of posets, i.e., a monotone function from the subgroup lattice
to the positive integers. We also investigate when the Chermak-Delgado measure,
restricted to the centralizers, is increasing.
