In an earlier paper, we have given a definition of the Rockafellar integration function associated to a cyclically monotone mapping considering only systems of distinct elements in its domain. Thus, this function can be proper for certain non-cyclically monotone mappings. In this paper we establish general properties of Rockafellar function if the graph of mapping does not contain finite set of accumulation elements where the mapping is not cyclically monotone. Also, some dual properties are given.
