Regular Multimeasures in the Vietoris Topology

In this chapter, for the case when X is a Hausdorff linear topological space, we first introduce and study for $$\mathcal {P}_{0}(X)$$ -valued monotone multimeasures, certain properties of continuity, such as increasing/decreasing convergence, order continuity and exhaustivity in the Vietoris topology. Then we compare these notions to those studied in the Hausdorff topology in Chapter 1 for $$\mathcal {P}_{f}(X)$$ -valued monotone multimeasures, X being a real normed space. As it will be seen, we shall obtain generalizations of certain previous results obtained in Chapter 1.