Integration of multifunctions with respect to a multimeasure (Q2709929)

Let \(X\), \(Y\), \(Z\) be Banach spaces and \((x,y)\mapsto xy\) be a bilinear mapping of \(X\times Y\) into \(Z\) such that \(\|xy\|\leq\|x\|\cdot\|y\|\). Let \(P(X)\) be the class of all nonempty subsets of \(X\). The authors study several properties of the integral \(\int_A F(t) M(dt)\) where \(F\) is a multifunction with values in \(P(X)\) and \(M\) is a multifunction with values in \(P(Y)\). In particular, there are given conditions under which \(\int_A F(t) M(dt)\) or its closure are convex. Moreover, a Radon-Nikodým theorem for multimeasures is presented.