Integral Representation of Continuous Comonotonically Additive Functionals

In this paper, I first prove an integral representation theorem: Every quasi-integralon a Stone lattice can be represented by a unique upper-continuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinitely many compact Hausdorff spaces with a collection of consistent finite marginals.