LAUSR

Abstract The present paper is devoted to study of the space of all weakly additive, order-preserving, normalized and positively-homogeneous functionals on a metric compactum. We construct an analogue of a modified Kantorovich–Rubinstein metric on the space O H ( X ) of all weakly additive, order-preserving, normalized and positively-homogeneous functionals on a metric compactum X . We prove that the functor OH is metrizable. We also show that for any metric compactum X the hyperspace exp ( X ) equipped with the Hausdorff metric can be isometrically embedded into O H ( X ) .