  A lot of research has been done on multipartite correlations. However, it
seems strange that there is no definition of so called genuine multipartite
correlations. In this paper we propose three reasonable postulates which each
measure or indicator of genuine multipartite correlations (or genuine
multipartite entanglement) should satisfy. We also introduce degree of
correlations which gives partial characterization of multipartite correlations.
Then, we show that covariance does not satisfy two postulates and hence, it
cannot be used as an indicator of genuine multipartite correlations. Finally,
we propose candidate for a measure of genuine multipartite correlations based
on the work that can be drawn from local bath by means of a multipartite state.
