  A characterization of t-normed integrals was obtained in \cite{CLM} for
finite compacta and in \cite{Rad} for the general case. Such characterization
establishes a correspondence between the space of capacities and homogeneous
respect t-norm monotone normed functionals preserving the maximum operation of
comonotone functions. In fact these theorems we can consider as non-additive
and non-linear analogues of well-known Riesz Theorem about a correspondence
between the set of $\sigma$-additive regular Borel measures and the set of
linear positively defined functionals. We discuss optimality of such
characterization.
