Radon-Nikodým theorems for additive interval multimeasures in Banach spaces

In this paper, we deal with Radon-Nikodým theorems for additive interval multimeasures defined on \(\mathcal {I}\) $\mathcal{I}$ and taking values in the hyperspace cwk(X), where \(\mathcal {I}\) $\mathcal{I}$ is the family of all closed non-degenerate subintervals of a fixed closed non-degenerate subinterval W of \(\mathbb {R}^{m}\) ${\mathbb{R}}^m$ and cwk(X) is the family of all convex weakly compact non-empty subsets of a non-separable Banach space X.