  Rado's Theorem characterizes the systems of homogenous linear equations
having the property that for any finite partition of the positive integers one
cell contains a solution to these equations. Furstenberg and Weiss proved that
solutions to those systems can in fact be found in every central set. (Since
one cell of any finite partition is central, this generalizes Rado's Theorem.)
We show that the same holds true for the larger class of $D$-sets. Moreover we
will see that the conclusion of Furstenberg's Central Sets Theorem is true for
all sets in this class.
