A sufficient condition is given for the existence of a strong \(\varphi\)-integrable uniformly bounded multifunction \(F:S\rightarrow Y\) such that a uniformly bounded multimeasure \(\Gamma:\mathcal A\rightarrow Y\) is of the form \(\Gamma(E)=\int_E F\,d\varphi,\forall E\in\mathcal A\), where \(\mathcal A\) is an algebra of subsets of \(S\), \(\varphi:\mathcal A\rightarrow Y\) is a multimeasure and \(Y\) is a specialized subset of the family \(\mathcal P\) of all nonempty compact subsets of a Hausdorff locally convex vector space together with a filtering family of semimetrics on \(\mathcal P\) defining a Hausdorff topology on \(\mathcal P\).