  A fascinating inverse problem that has been receiving considerable attention
is the construction of realizations of random two-phase heterogeneous media
with a target two-point correlation function. However, not every hypothetical
two-point correlation function corresponds to a realizable two-phase medium.
Here we collect all of the known necessary conditions on the two-point
correlation functions scattered throughout a diverse literature and derive a
new but simple positivity condition. We apply the necessary conditions to test
the realizability of certain classes of proposed correlation functions.
