Non-linear operators on sets of measures

Summary If M[ℬ, U(C, C)] is the collection of U(C, C)-valued (non-linear) set functions defined on the Borel subsetsℬ of the compact Hausdorff space S, one may define operators on M[ℬ, U(C, C)] which are ? of the Hammerstein type ?. We initiate a study of a concept analogous to the second dual of a space of continuous functions by inquiring as to what representation theorems one may obtain for these operators. A ? Lebesgue type ? decomposition theorem for elements of M[ℬ, U(C, C)] is obtained. A ? density ? theorem is also obtained for the space M[ℬ, U(C, C)]. Entrata in Redazione il 6 marzo 1974.