On some metrics compatible with the Fell-Matheron topology

Modifying the Hausdorff-Buseman metric, we obtain a compatible metric with the Fell-Matheron topology on the space of closed subsets of a locally compact Hausdorff second countable space. We also give an alternative expression of this metric, and two more compatible metrics, a metric of summation form and a modified Rockafellar-Wets metric. Through the study of the relation between the original Hausdorff-Buseman metric and the Rockafellar-Wets metric, it is also shown that the convergence in the original Hausdorff-Buseman metric in the space of non-empty closed subsets of RN is equivalent to the Painlevé-Kuratowski convergence.