  In this paper we present a measure of quantum correlation for a multipartite
system, defined as the sum of the correlations for all possible partitions. Our
measure can be defined for quantum discord (QD), geometric quantum discord
(GQD), or even by the entanglement of formation (EOF). For tripartite pure
states, we show that the multipartite measure for the QD and the EOF are
equivalent, which gives a way to compare the distribution and the robustness of
these correlations in open quantum systems. We study dissipative dynamics for
two distinct families of entanglement: a W state and a GHZ state. We show that,
while for the W state the QD is more robust than the entanglement, for the GHZ
state this is not true. It turns out that the initial genuine multipartite
entanglement present in the GHZ state makes the EOF more robust than the QD.
