Some remarks on characterization of t-normed integrals on compacta

A characterization of t-normed integrals was obtained by Luis M. de Campos, María T. Lamata and Serafín Moral (1991) for finite compacta Radul (2022) the general case. Such establishes a correspondence between space capacities homogeneous respect t-norm monotone normalized functionals preserving maximum operation comonotone functions. In fact, we can consider these theorems as non-additive non-linear analogues well-known Riesz Theorem about set σ-additive regular Borel measures linear positively defined functionals. We discuss optimality such characterization.